The discussion does tend to go around and around in the same tired circles on this subject; a bit like the subject of chain fires.
I would suggest that those who swear by nitrate saturated paper take care to keep the nitrate salts in the same general fuel/oxidizer ratio as gun powder, since extra nitrate only contributes to additional fouling.
Embers are a problem, and wadded paper even if treated with nitrate is perfectly capable of creating an ember. Keeping the cartridge thin, whether treated or untreated is simple common sense.
I haven't tried commercial flash paper, but can state from experience that nitrocellulose, which is what flash paper is, is far superior to ordinary paper, whether nitrate saturated or not, in the making of combustible cartridges. They always fire and don't leave embers or ash.
An issue with flash paper, whether home-made or purchased is that cellulose is extremely absorbent, and the fibers can hold residual acid even if the paper appears dry. The residual acid can cause spontaneous combustion of the paper. This bit of chemistry should be kept in mind by those inclined to make up a large supply of combustible cartridges employing flash paper. I have read that commercial flash paper is shipped wet, and after drying by the end user has a limited shelf-life.
Considering the amount of paper consumed in the construction of a carefully made cartridge, commercial flash paper might be worth trying. My suspicion is that it's nitrated tissue and probably not mechanically substantial enough to readily form into useful cartridges, perhaps double wrapping would work.
I would not suggest wrapping flash paper up over the bullet, lower grades of nitrocellulose paper generally don't ignite past a pinch-point, but one never knows.