Roundball, load some BP cartridges and hunt with the Colt. That is one of my past times and I enjoy it very much. I now use a very tight stevens 16 gauge but have used a couple of old 12's. One I had to reglue and fill in cracks on the stock. It was tightened with a hammer at the lock up point. It is the same as shooting a percussion double only you can unload and clean easier at the end of the day. Shot a lot of ruffed grouse with these guns. One would just about cover a car door at 25 yards. To load BP cartridges all you really need to buy is a roll crimper and a few wads. You can make the decapper and primer seater.
As to using modern barrels for the flinter, it is a matter of determining whether you want to build a iron mountain Southern rifle or a Golden age engraved and carved flinter. I would suggest that for a first try you might be better off building with a modern style set of barrels as it takes a couple to learn how to do it. As to the chamber flare that is very true on modern barrels but I have a Stevens 311 taht does not have one. Also Taylor S made a good point about gauge. For quick use in the field, on pheasants for instance, unless you have large hands, a smaller gauge like a 16 is nicer to reach across for cocking. A 14 gauge makes a lot of sense in this type of gun as it has about as much hit as a 12 and is more compact. They used to make a 14 gauge cartridge for this reason and us die hard 16 users do so for the same reasons.
DP