First, I would say that bias and flat frames are fairly critical. Dark frames may be critical they may not be, there are a few factors that play into that. All of these frames are calibration frames, as they allow us to "calibrate" each and every light frame.
Starting with definitions.
A bias frame is a frame that represents the bias signal of your camera. As far as I know, all cameras have a bias signal, which is a generally fixed pattern that exists due to the physical and electronic traits of the sensor's design. In general, there is some base voltage applied to the sensor in order for it to operate correctly (you need a voltage applied to each pixel in order to give each pixel the potential to release electrons in response to the energy of incident photons). In DSLR cameras, a bias signal (when stretched enough) is often dominated by some kind of banding structure. In CCD cameras, a bias frame could be very clean, or it may contain some kind of pattern...it depends on the quality of the camera.
A dark frame is a frame that represents an exposure done in total darkness. This signal includes the bias signal, but also includes any dark current charge accumulation, and thus any dark current noise that exists within the dark current signal. In both DSLRs and CCD cameras, accumulated dark current tends to reveal another form of fixed pattern noise...hot and cold pixels. Dark current is additional signal, on top of the bias signal and on top of any image signal you would have in a light frame. That additional signal accumulates faster as temperatures rise, revealing more and more hot pixels.
A flat frame is a frame that represents the field flatness. Unlike bias and dark frames, flat frames are not about noise, they are about identifying the "shape" and structure of your field. By field, I mean the area within the frame. A field may be non-flat due to a couple things. First, there is usually some amount of vignetting unless you are using a very small central portion of a very large image circle. In many cases, the image circle of a scope will barely be large enough for sensors of approximately APS-C sized (i.e. a 7D II, or a KAF-8300). In some cases, the image circle of a scope may be huge...as in the case of the Tak FSQ106, which has an 88mm image circle, and is unlikely to produce vignetting on either of those cameras. Flat frames also represent the dust motes on your sensor, which affect the cleanliness of your field.
What's Absolutely Necessary
Are all of these frames truly necessary? Personally, I believe that, at the very least, you should be correcting your field flatness in every image. Subtracting darks may or may not be beneficial, there can be a number of factors that play into whether they are or not. If you have low dark current (i.e. with a thermally regulated CCD, or DSLR in cold winter months), you may not have much dark signal to worry about in the first place. If you dither and integrate with some kind of sigma clipping algorithm, you might not need dark frames even if you have higher dark signal. So, darks are not necessarily critical...but more on this in a bit.
Back to flat fielding. Vignetting can greatly darken the corners of your image, and as you integrate more and more light frames, that darkening becomes more pronounced (i.e. in the center of the frame, you may be integrating fairly strong signal of say 2000ADU, where as in the corners you may only be integrating very weak signal that might barely be above the read noise floor at 50ADU....add ten frames, your center signal becomes 20,000 ADU, but your corners remain at a mere 500 ADU.) Flattening the field of each individual light frame can greatly mitigate that exaggeration of vignetting when you integrate by brightening the vignetted parts of the frame.
So, if only flat fielding is necessary, why did I say biases are also critical? To properly calibrate lights with flats, both the lights and the flats must first have the bias signal removed. This is important because flat frames must usually be scaled first in order to be effectively applied to each light (this is usually called normalization.) Scaling the flats will change the bias signal in the flats...so before that scaling is performed, the bias signal must first be removed. If the bias signal is removed from any calibration frame, it must be removed from every single frame involved in an integration. That includes lights and darks.
Flat frames are usually divided out of your light frames, rather than subtracted, which is how vignetting and dust motes are corrected (if you think about the math, it makes sense. If you consider the pixel values in your flat being from 0 to 1.0, and the corners of your flat are 0.025 while the center of your flat is 0.8, dividing the flat out of each light balances out the field: 2000ADU/0.8 = 2500, 50/0.025 = 2000.)
So, to properly calibrate light frames with flat frames, you need bias frames. There is an alternative. Instead of using bias frames, you could calibrate each flat with flat dark frames, which subtract dark frames matched to the temperature and exposure duration of the flats. Personally, I find using flat darks to be a lot more work, especially with DSLRs where you may need new flat darks every time you create new flats. Bias signal doesn't change much (it can, but usually very slowly over very long periods of time, months or years), so one master bias is often sufficient to calibrate everything.
More on Dark Frames
Getting back to dark frames. Do you need them? You may, it depends. For the most part, dark current reveals hot and cold pixels. Some pixels are "hotter" or "colder" than the average due to differences in the response of the silicon in each pixel. Some pixels will accumulate additional charge from both dark current more readily than others. Some pixels will accumulate charge more slowly. Darks, when subtracted from lights, will subtract the additional charge that accumulates in hot pixels.
There is a consequence to subtracting darks like this. Unless you take an exorbitant amount of individual dark frames to integrate into a pristine master dark (and were talking a few hundred frames), dark frames will also contain some random noise as well. Subtracting a master dark from a light will correct the hot pixels, but it will also make cold pixels colder, and it will increase the standard deviation of the signal, increasing the random noise in the light frame. In practice, the increase in random noise may not be enough to be of consequence, particularly not when using thermally regulated CCDs or DSLRs in cold winter temperatures. During hotter weather, the increase in random noise from dark subtraction with DSLRs could become a problem.
There is another way to eliminate hot and cold pixels (as well as any statistically unwanted outlier signal, such as cosmic ray hits.) Dithering. With dithering, which is a process of offsetting the stars a little bit in each light frame, special algorithms that will "naturally" reject hot or cold pixels can be used when integrating your calibrated lights. More on dithering a little later.
Sometimes sensors accumulate other unwanted signal as well. Glows, for example. Amplifier glow, which is caused by increased dark current due to the uneven heating of the sensor die by other electronics, say a poorly shielded DSP on a motherboard located too near the sensor. This additional signal, often presenting as a hemispheric bubble of increased dark signal, or a brightened sensor edge, can only be removed by subtracting it out with dark frames. There can be other kinds of glow as well, such as the 5-point glow issue with QSI's Sony-based CCD cameras. Dithering will not be sufficient to affect glow signals, so darks are your only option. If you have an issue with some kind of glow, then you should calibrate your light frames with darks as well as flats. Since the flats must be calibrated with biases every individual frame, each light, each dark, each flat, should first be calibrated with a master bias.
What are master frames?
I've mentioned master frames a few times. When you calibrate each light frame, a "master" bias, "master" flat, and possibly a "master" dark should be used, rather than one single bias, flat, or dark frame. What is a mater calibration frame, and why are they necessary?
Every frame you create with your camera will have some amount of random noise in it. Primarily read noise, this random noise can actually be a bit of a problem for your lights. Subtracting a single bias frame, for example, will remove the bias signal, but the random noise in the bias will subtract from the random noise in the light. Random - random = even more random, as tends to be the case. That may be inaccurate...what it really means is subtracting random noise from random noise results in an increase in the standard deviation of pixel values, which means more noise, not really more random.
A master calibration frame is the integration of many individual calibration frames. A master bias, therefor, is an integration of many bias frames. A master dark is an integration of many dark frames. A master flat is the integration of many flat frames. How many frames should be integrated for each master? There are different schools of thought on this. In general, a couple dozen flat frames and dark frames are enough to produce a good master. Personally, I use 30 flat frames for my master flats, and when I was using darks I used 30 dark frames. Some imagers use only 10, others use more. The general idea is to reduce the random noise in your master calibration frames. Noise is reduced as the square root of the number of frames integrated. Integrating 10x results in a reduction in noise by a little over a factor of 3, integrating 30x reduces noise by nearly a factor of 5.5, integrating 50x reduces noise by a factor of 7.
How many bias frames to integrate into a master bias is sometimes a more controversial subject. Again, some imagers integrate a mere 10 frames, others maybe 30-50. Some imagers will integrate 200-300 frames. Why so many? Subtract a semi-noisy bias from a dark, that increases the random noise in the dark. Subtract both a bias and the dark from a light, and you increase the random noise of the light even more. There is something to be said for having a truly pristine master bias, one largely devoid of random noise. Tests have shown that integrating ~180 bias frames results in a very clean master bias, and integrating ~360 reaults in a totally clean master bias. If you have the patience, creating a very clean master bias can mitigate any increase in random noise when calibrating your lights with a master dark. It should be noted that there are ways of creating a "superbias" frame, which takes a minimal number of bias frames and agorithmically creates a master bias frame that is as clean as if you integrated thousands of bias frames together. This is the most effective way of creating a super clean bias, without having to expend shutter actuations on your camera or burn cpu cycles creating a massive several-hundred frame master bias.
Calibrating and Integrating
When it comes to actually calibrating your images, there are a few things to know. First, for the most part, there are existing tools that will do most of the nitty gritty work of calibrating your light frames for you. DSS, as well as PixInsight's BPP (Batch PreProcessing script) will handle both the creation of master calibration frames, as well as the actual calibration of your lights, for you. All you really have to do is generate the individual calibration frames and load them into DSS or BPP properly.
For integrating your master calibration frames, it's best to use some kind of median replacement sigma clipping algorithm. A sigma clipping algorithm is one which will identify and reject or replace "statistical outliers", or pixels that deviate too far from the expected mean. When generating a master dark, for example, the Median Sigma-Kappa integration in DSS, or Winsorized Sigma Clipping in BPP, will average out random noise, strengthen hot and cold pixels and any other fixed patten, and reject any other statistical outliers...such as a hot pixel or group of pixels that only showed up in one frame (i.e. a cosmic ray hit). This generates a master dark with low random read noise, and a very strong signal for the fixed pattern and/or glow signal that the master dark is intended to remove from each light frame.
The same integration algorithms should be used to create your master bias and master flat frames as well.
Once you have your master calibration frames, you will then need to calibrate your other frames. Generation of a master bias should be first (and usually will be, automatically, with DSS and BPP). Once the master bias is created, it will be used to calibrate each individual dark frame via subtraction. The same goes for each individual flat frame. Once all the dark frames are calibrated, a master dark will be created (if your using darks). Once all the flat frames are calibrated, a master flat frame will be created. You now have all of your master calibration frames.
One you have your master calibration frames, you can calibrate your lights. First subtract the bias, then subtract the dark. When subtracting the dark, a procedure called "dark scaling" may be applied. When using dark scaling, the use of biases is a must, since the master dark will be adjusted in brightness to better match the level of identified hot pixels in each light frame. When using DSS or BPP, this scaling will usually be done for you, however you may have the option to override it and manually choose a scaling level.
After subtracting out the master bias and dark frames, divide out the master flat. When using DSS or BPP, the master flat will usually first be normalized to each light frame. This simply means the brightness level of the flat is adjusted to more closely match the brightness levels in the light frame. After dividing out the master flat from each light, you should have a set of fully calibrated, flat fielded light frames devoid of vignetting or dust motes.
Your light frames are now ready to be integrated. By removing bias signal, hot pixels, fixed pattern noise, and vignetting and dust motes, you preemptively head of the creation of more severe issues in your final integrated image. Integration (the averaging together of the pixel data from each light frame) is a process that reduces noise, but reinforces structure. Fixed patterns, such as the banding of the bias signal, the hot pixels and glows of dark current signal, and the vignetting and dust motes of your field, will all become reinforced and more pronounced during the integration process.
If you do NOT calibrate your light frames first, these issues, which may only be mild in each individual light frame, could and likely will end up being much, much more significant in your final integration. A dust mote, for example, that barely shows up in a single light frame might become a pitch black "dark hole" in your final integration. Faint banding in each light frame might become very strong, pronounced banding in the final integration. Calibration of each light frame BEFORE integration minimizes or eliminates these artifacts, these unwanted structures and patterns, before the integration of your light frames...so they never become reinforced.