The majority of antique flintlock pistols I'm familiar with don't have a hooked breech, lug for attachment to the stock, or a tapered octagon barrel. There is no such thing as a standard pistol, but here is a picture of an antique flintlock with a pinned barrel.
It's hard to see, but this gun has a tapered, octagon to round barrel, with a wedding band at the junction, and you can see the pin just in front of the wedding band, in the wood. The top picture has the best view of the pin because it's shinny in that picture. There are other hard to see pins, but there are pins holding the ramrod pipe and entry thimble to the stock. Like I said, nothing is standard, but this type is common, along with lots of all round barrels. So I did some research, and I found this picture of a French pistol circa 1800.

There is no way to tell if this gun has a hooked breech, but it has a tapered octagon barrel. Note the barrel has a slight flare at the muzzle. This was done on purpose on both the round and octagon barrels, not standard and not common, but done on more than you might think. Also note the barrel is attached by lugs, one halfway, and one near the muzzle. I have no idea if the barrel had burst, it's possible with an obstruction, but more probably it's just rusted away, but what you think might have been caused by a bursting barrel could have been built into the barrel when it was new. Can you get a measurement inside the bore, so we can try and get an idea of the caliber. Regarding the vent liner. Most likely the vents started out life as a drilled hole in the barre, which meant the fire in the pan had to flash through the thickness of the barrel. With a vent liner, it could be cupped on the inside and it's reasonable to suppose the gun would go off just a fraction of a second faster, which is important when you are trying to hit what you are shooting at. The reason there is no screwdriver slot in the liner is because it was screwed in to proper depth, then cut off and filed smooth with the barrel. Hope this helps.