As someone with a lifelong interest in old musical instruments, this is an intriguing item .I like j42's "palpable antiquity ".
If it's a fake , it's been done by someone with a pretty deep knowledge.
While I can only judge from the photos, the shell appears to have been made from a single slice of wood. All wooden drums since the 19c century have been made from plywiood because of the extreme difficulty of getting a slice of self-wood big enough to form a shell, and because forming it from plywood is just so much cheaper and easier .
The skins are convincing, as is the hempen rope ( again , something very hard to find recently ) , and the way it has been fitted in every detail, something that only a professional drum maker would know.The tightening buffs are again perfect. The distortion is also something that happens to hand made instuments, as is apparent if you look at "ethnic" drums .
The paintwork is actually redolent of much period decorative work, done really quite quickly. It reminds me of Tudor household decoration , which survives is odd corners of historic houses .Which is not to say for a moment that it's that old .
I think the drum is genuinely old, but as to what precise date I couldn't say... but pre industrial tools and machinery, which puts it at least into the early 19century.
It could possibly be an "ethnic " item repainted, except that the construction is exactly that you would expect of an 18century European drum rather than something from Africa of Asia .
The paint colours are also entirely period . Their thin application in places is nothing unusual , it happens when you work in oils. Granted that 19c and more recent Regimental drums are painted to a MUCH higher standard than this, but that takes a lot of time and trouble, and this might not be quite in that class.The painting is perhaps the least convincing part , but that doesn't rule it out as original .
One might finally ask why anyone would go to the trouble : this would have taken perhaps ten days or more to make from scratch,obtaining the materials would have been damned hard , and the profit might be a little thin for that amount of work