"It depends". In general, I would recommend doing flats if you change anything; however, if there are no dust spots on an optical surface close to the camera, and any vignetting pattern does not change as you rotate the camera, then you can get away without shooting flats at different position angles.
Hi, in the FWIW category, I've done a good bit of experimenting on this issue. I get pretty good results for pretty picture imaging without worrying about the rotation angle provided the flats are relatively recent. However, my system seems to be very symmetric. I'd suggest doing a test flat at a few rotation angles one after the other (assuming you are using a flat panel and not the sky) and then using pixel math or something similar to subtract them and see what you get. I suspect you'll then be able to tell whether it will work for you. Edit: I should add that I try to get flats at the exact rotation angle when I can notwithstanding what I said above, and always for photometry work.
Mark run an engineering test. Do 10 known non-variable targets over the sky with different check stars, 20 if you have a GEM so you have to flip. All different places (across the sky). Do each target at 2 or more PA’s like 0 and 90. Reduce the photometry and compare with a gold standard. Like do this on APASS stars or something. Is your photometry “good enough”? Then you’ll know the answer and not guess or spend a bunch of useless time over-doing it.
Hi Bob, I did that some time ago when I was doing exoplanet transit follow up. For that work flats rotated 180 after a meridian flip were ok to use I found. Other than for i’ and z’ band, doing flats isn’t a big deal for me because I have a flat panel. It is more work for the i’ and z’ since it doesn’t put out any flux in those bands and sky flats have to be done. With ACP even that’s not a big deal now. I will check again on this with the new camera I’m using now. Thanks for your suggestion.