The earliest year shown for a US pistol in "Flayderman's Guide to Antique American Firearms" is 1799, referring to the 1799 Flintlock Pistol by North & Cheney.
This pistol was in production from 1799 thru 1802. Its design was based on the French Model 1777. The lock was an integral part of the brass receiver and it has a round tapered barrel, large at the breech tapering to a smaller diameter at the muzzle.
In the "Secondary Military Single Shot Pistols" section of the book there are two pistols that are earlier than 1799.
The "Ezra Dodge Flintlock Pistol" was made in New London, Connecticut from 1780 thru 1790. It was a large holster pistol 12 1/2" long and had a "Thick walled 7" octagon brass barrel; caliber 44. Matching brass lock plate with integral brass flashpan marked in deep sunken hallmark in center "DODGE" with small sunburst design each end."
The other early Secondary pistol shown is the "Hodgson Flintlock Pistol". "Circa 1790's (possibly earlier) to 1800/1802. It has a 9", part octagon, part round brass barrel marked in bold script BALTIMORE CALIBER 60. The cock (hammer) is a goose neck style.
The muzzle end of the barrel has a small, larger, ring shape to it but it is not at all a flared blunderbus shape like the pistol in the OP's post.
