Flats: This is where it gets tricky. Flats by definition define the transfer function of the imaging setup. A master flat includes both linear and non-linear components. A dust Mott being an example of a non-linear component. This is really a cleanliness issue! A dust speck on the outmost surface of the telescope will cast a very faint shadow and not likely be visible in a stacked light master, while a water spot on the glass cover of the camera will cast a very deep shadow. That said, if after calibration and integration and there are no non-linear imperfections, and one finds DBE necessary, one will achieve better results from not using flats. Instead, DBE if done correctly, will precisely remove vignetting ( radial gradient), even with a lot of nebulousity. To do this precisely with a master flat is very difficult because the master light is being divided by the master flat. All sorts of additional problems of a non-linear nature can be introduced by this operation. Again, if after calibration using flats, DBE is still required to remove gradients then the image has likely been degraded by the calibration process.
Not sure who said you can get better results with just DBE and no flats...but I VERY, VERY, VERY STRONGLY disagree! Having had to deal with correcting issues like dust motes and even vignetting with DBE in the past, along with LP gradients, I speak from experience and can tell you it is NOT an easy task, and 99% of the time you will lose your data set and be unable to get a good result if you do not calibrate with flats.
Yes, it CAN be possible to correct dust motes with just DBE...it is extremely difficult and usually requires an extremely, extremely dense net of samples, along with multiple passes of correction with aggressive settings. Such a DBE-only correction is usually only possible with a largely empty field...i.e. globs, galaxies, and only when they do not fill the frame. Even in such images, the level of DBE gradient removal that has to be applied is usually devastating to any other structure in the field, and tends to make the field look unrealistic in the background signal (I've done it on more than one occasion). To be quite blunt: any field full of object structure that also has transfer issues that flats normally correct for, is IMPOSSIBLE to fix with just DBE. DBE cannot on its own separate dust motes, vignetting and other shading from other structure in a packed field.
Consider:
Original field (mis-corrected dust motes...flats were from a slightly rotated setup, accidental! The ONLY time I would recommend even trying this!):

Field with extremely dense net of DBE samples applied:

(Imperfectly) Corrected field:

The field is corrected, but also too flat overall, but still not fully corrected in several areas. Even after all that effort (immense effort) to build that dense network of samples.
There is another reason to use flats as well. Flats correct for another kind of FPN. Where darks correct for DFPN which is the result of DSNU (dark signal non-uniformity), flats correct for FPN that is a result of PRNU (photo response non-uniformity.) Flats and only flats can correct for this kind of FPN. Note that as you stack more, this kind of FPN, if left uncorrected, can limit SNR much sooner than DFPN. A lot of the time, this kind of FPN is very gaussian so it is one of those "unseen restrictions" on uncalibrated data. Again, dithering can randomize this pattern...but then you have another source of noise (in addition to the normal noises, as well as in addition to DFPN.)
Calibration is not an optional thing IMHO. Calibration is an essential part of the process of CORRECTING your raw data so that it can be processed correctly, and so that you can minimize the amount of noise in your data and maximize your SNR. DBE is not even remotely an alternative to flat frames for correcting field issues. Flat frames are exact and know everything about exactly what they are intended to correct, DBE can only model based on the data, it has no prior knowledge of the issues you wish to correct with it, and thus it is your job, the