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you need a different master flat for every imaging configuration: lens/scope-filter/nofilter-camera(if different ones, even of the same exact model)-component relative orientation (eg if using a nosepeice or rotating camera mount for framing), but not for every target.
The flats (which you take a few of and combine into a master in the interests of averaging) are a sample of the path taken to each pixel by "identical" (hence "flat field") photons from the end of the sky to the start of your sensor, so that you can remove the variation your equipment introduces and approximate "what the sky would look like if your optics were perfect". Any change above the bottom of the sky (your choice of target, the atmosphere etc.) or below your sensor (the camera's amplifier bias, dark current etc.) are not the responsibility of the flat field to correct.
Rotations of sensor vs lens/telescope objective do matter, more the a) dustier/damaged the glass b) greater the number of optical elements, since nothing is perfect. Think about things like the inevitable nicks and shiny spots in the felt/baffling inside the OTA, or how many not-completely-blacked lens edges there are in an SLR lens. I tell people not to reuse flats between nights at the observatory for the simple reason that even if we left the camera attached (we usually don't), we park the scope, so the dust inside has all day to settle differently.
OK, that might sound like an argument for flat fielding again each time you switch targets, but there's also a "within reason" element to our use of time...
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