Very interesting that it could be from Birmingham. Didn't use a bore scope but used a small flashlight and looks to have been a smooth bore.
After reading your excellent comments, would a date be closer to 1830 or later?
I forgot to include a photo of the rear sight...
I am not an expert. I've just been looking at a lot of late-flint English sporting rifles for a while learning about them. Scores of them. Every one I can find online, the auction sites are full of English flintlock guns and rifles if you look hard enough.
I have not seen an English rifle with all those features plus that long a barrel. Only English smoothbores. And generally those were round or half-round. It looks like Tryon was importing by 1832. I don't know if he imported earlier than that, it might be possible.
Birmingham made guns "for the trade." On another thread I posted a W. G. Chance flint rifle from Birmingham that had the London rifle features that became classic plains rifle features. W.G. Chance had a NYC office that forwarded trade goods to St. Louis and was a vendor to the American Fur Company.
I'm guessing that your gun was made for export, and what is true of dating London rifles might not hold for exported Birmingham rifles. But my guess is that 1830s sounds possible. Earlier than that there wasn't as much importing and later a caplock would seem more likely. Also, if this gun was made for export it's possible they made a long rifled barrel for the American market. Typical English rifle barrels in the early 19th Century were 31" , when American barrels were much longer. The short barrel appears on plains rifles with a lot of other English features. The WG Chance rifle had far more drop than typical English rifles, yet the stock was evidently original because the butt had been narrowed to fit a crescent plate. That stock and your barrel are anomolies in English guns, but align with American tastes. Meaning Birmingham might have been accommodating the American market a little.