Regarding mottling in flats.....
Without the intention of any specific hypothesis to test, I happened to have used a friend's Astrodon 3nm Ha filters and my own Baader 6 nm Ha and taken flats on both. My observation was that the mottling appeared on the 3 nm filter but am not seeing this on the 6 nm filter.
Thinking about the high contrast expected in the 3 nm filters, this could bring out any slight irregularities in the sensor's AR coating. Perhaps also coupled with the longer wavelength in Andy's hypothesis and Lead_Weight's observation, this could be an impact causing the mottling.
But it also seems to me that if any/all of the hypotheses are correct, than flats absolutely would calibrate the image. (Since the pixel non-uniformity would be fixed in the pixel array and not random.)
I've only see it appear in my narrowband light subs of HA and SII, but not in OIII. And it's not appeared in any broadband images for me.