Hot soapy water is still one of the best cleaners there is for black powder fowling. It removes it, and is cheap to use. It is more commonly used with traditional rifles although I use it as a basic cleaner with my inlines as well. The way described, with the cleaning patches works just as well.

The main thing with what ever method you use, get ALL fowling out of the barrel. From time to time, a bore brush with solvent to remove copper, lead, & plastic traces is a good idea. After you dry patch the barrel and the patches come up clean, coat that barrel with a very high quality gun oil. Now some people use bore butter and that's fine, their rifles. I know a fellow that uses 10W-30 motor oil. He claims it does the same thing. Again, his rifle. I use Birchwood Casey Sheath a.k.a. Barricade, or Rem Oil with Teflon, among some. The main thing is get that metal coated. Also be sure to wipe the outsides off good.