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Something not mentioned about the white clothe is it needs to be taut and uniform across the end of the telescope/lens, no sagging or wrinkles or overlaps as these introduce false artifacts that will get removed from your shots.
Second the screen needs to be flat/perpendicular to the end of the setup. In your shot above its angled to the end of the scope, this will introduce a false gradient.
Instead of white clothe you may get better results making a "filter" to slip over the end of your scope with say a piece of plumbing pipe with a piece of stiff tracing paper glued across the end. I've used tracing paper for years for making light tents for diffuse light photography.
Of course you really must take flats at the time you take subs as dust on the imaging sensor changes if you are putting a camera body on scope then using for regular photography too. Only if the body is 100% dedicated and permanently remains attached will flats taken at other times be of use for just removing "dust on sensor" artifacts only. "dust on the end of the lens" "front refractor element" or "mirrors in refractor" you can expect to change all the time as these are typically exposed to the air, even if you clean each time stuff ends up settling out of the air anyway. Which is why its important to take flats as part of the imaging session rather than another time as the dust pattern will differ.
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