Just finished cleaning it. First I ran hot water through the barrel and cylinder. Then I soaked it all in moose milk (a mixture of Ballistol and water) inside and out. Then let it sit for a while. Then scrubbed the chambers and barrel, and wiped everything inside and out, leaving a slick film of Ballistol all over, and inside. I greased the cylinder pin (arbor?), then reassembled it and wiped it all down.
Don't forget to pull and clean the nipples (cones). If neglected, after a while they will practically weld themselves to the cylinder and you will have to heat them with a propane torch to get them out. That is IF you can get them out at all after they seize up. I strongly suggest after cleaning them, add a drop of Breakfree to the threads and pull and clean them after each shooting session. Black powder pistols are fun to shoot, but a damn pain to clean! Also, very unforgiving if not cleaned properly.