Hello,
I think the main thing to remember is to be diligent whatever method you use. Clean the gun immediately, oil well, and check the next day.
There is no difference in percussion cleaning versus flint. The difference comes in whether you have a pinned-in barrel versus some sort of hooked breech that is easily removed.
Wade wrote "Plug the hole with a toothpick--shortened or you'll snag it and leak funky water. Fill the barrel with water and let it soak for a bit. Pour it out. repeat if you like. At some point wrap some tow on a tow worm and run that a few times. repeat until clean. Tow can be rinsed out and re-used. Dry it out with water displacing oil and then apply rust preventative and you're done. Unblock the touch hole."
This is a good basic plan. I differ a little so let me elaborate.
I have used a toothpick to plug the hole for years (it works), but recently got a strong wafer-shaped rare earth magnet (thank you Ron Hess). I cut the finger off of a surgical glove, and dropped the magnet inside the finger tip. The rubber is for a seal. Place the magnet/fingertip over the touchhole and it seals off any leakage. I like it a bit better than a toothpick. If you use a toothpick, fold a patch over it to catch any fugitive drips, and trap pick/patch both in place with the frizzen.
Stand the gun up, and use a funnel to fill the bore. DO NOT USE HOT WATER. There is no advantage to hot water, as lukewarm cleans just as well. Hot water can/will flash rust your bore. Why chance it? I don't know where this hot water idea came from, but it has persisted.
I have also recently converted to using cheap blue windshield washer fluid (thank you Bob) for cleaning, and it seems to work faster than plain water. Let the fluid sit in the bore for a few minutes, slosh back and forth with your thumb over the muzzle, and pour out.
At this point I run a nylon bore brush back and forth a few times. I then refill and let sit for 5 minutes. Pour that out.
I do not use tow for cleaning, though some do. I find a good brass jag with Butch's Bore Shine cotton twill patches to fit the bore tightly and do a great job of getting in nooks and crannies (corners of the grooves). I just use those patches with blue washer fluid until the bore comes out clean. I find adding soap makes a foamy mess with my cleaning.
IMPORTANT STEP - I dry the bore, then wet patch it with Mr Flintlock lube, or LVL, which will remove any graphite left from our blackpowder. This will usually reveal black on patches that did not come out with the washer fluid. Graphite. Thank you Mad Monk.
Dry the bore, and lube it well with WD-40 for moisture displacement.
The following day, wipe out the WD-40 moisture displacement and replace it with your bore preservative oil of choice. There are times that you'll see a light bit of surface rust on the second day, depending on humidity conditions. Hence the second day checkup and wipe out.
REMEMBER - That black-filled water from the bore can flat out ruin a gun's finish. Be very careful when handling that wet stuff to keep it off the wood. It can also quickly turn your brass black. Just fair warning for newcomers. For that reason I tie a microfiber cloth around the breech to catch any drips that might run down. Once you've seen a light colored wandering line down a stock, you'll want to make sure it doesn't happen to you.
This is my procedure based upon experience and the advice of others who are successful. I hope this helps. God Bless, Marc