Being its a flintlock use only black powder. Even the rifles that claim the can shoot substitutes normally end up duplexing with black powder. So why not use the powder made for flintlock rifles. Depending on your rifle it might like FF or FFF. Only testing will show that. I would start with FF first if a .50 caliber, FFF if under .50 caliber.

Many of the T/C rifles have a 1-48 twist. You don't mention the model. There are a few that have a slower 1-66 twist. But both of them will shoot round ball. Get some .490 roundball if .50 caliber. 530 roundball if .54 caliber. A .015 patch is a good start. You might have to get thinner but I doubt it. As for the lube, spit works. Olive oil, Liquid Wrench, Mink Oil, and countless others. Yes and even bore butter works.

Start testing your rifle with 80 grains and work up 5 grains at a time. I will guess the best groups are around 85-90 grains of powder and a patched ball.

Keep your flints sharp. use at least 3f in the pan... 4f is better. In my T/C flinters they like their pan powder on the outside edge of the pan. If you get too close to the touch hole they tend to fuse fire.

Other then that, swab between shots if you have to and have fun.