Scout, what kind of flinter you have will help you determine the best way to clean it. If it's a "pinned" barrel, taking it down for cleaning is not only a real hassle, but will eventually cause the pins to loosen up. Also, some of the touch hole liners can't be removed without taking off the lock and that gets to be a hassle too, although preferable to removing barrel pins.
My cleaning process does not involve a bucket of water or pumping action or any of the similar cleaning styles.
I plug the touch hole with a toothpick and pour about half a barrel full of cold water and plug the bore and tip the gun back and forth several times and pour out the dirty water. I do that about 3 or four times until the sloshing doesn't remove any more crud. Then I scrub out the bore with a mild soapy water mixture and a bore brush and I use a smaller brush for the chamber area. When I'm sure I've cleaned out the innards, I rinse a few times using the same sloshing technique. Last, I pour extremely hot water in the bore to the top and let it sit until the steel has heated up real good and pour it out.
I dry the bore and while it's still really nice and hot, I use my metal preservant.
One way I have found to make sure the chamber area is good and dry is to heat up a small patch jag from a .22 or .30 depending on your firearm's caliber. The jag must be small enough to fit down into the powder chamber easily. I heat one up with a hand torch intil it fairly glows and I drop it down into the chamber to do its work. It dries things up nicely down there!
I give it a squirt of water displacer and the gun goes into storage until the next time.
No rust...no muss...so fuss.