As I understand it, you have nothing but a barrel. The fire story in interesting, or perhaps the barrel was never even on a gun. If it was in a fire, it is probably ruined as a barrel and maybe warped.
(I can't see a rifle being used to get a "bunnyburger"; that is what shotguns were for and it has been said with a lot of truth that the shotgun, not Winchester or Colt, was truly the "gun that won the west", or at least kept the pioneers fed while they were doing the winning).
You might be able to find one of the makers of flint/percussion rifles who are around today, and see if he would build a rifle around the barrel. But if he will, hold on when he gives you a price! If you are handy, you might get a Dixie Gun Works (
www.dixiegunworks.com) catalog. They have stocks, and the other parts you would need to build a rifle, but I warn you it is a lot of work, and you have to include some specialized tools in the cost.
One thing I think is pretty sure, is that the Remington barrel pre-dates the Civil War, probably by several years. Before, during and after the war, Remington went to mass production, first of military muzzle loaders, then of cartridge guns (mostly the rolling block) and stopped making muzzle loading barrels or guns for civilians.
Jim