Here's what I did on a Dan Wesson .44 magnum, worked like a charm. I don't see any reason why it wouldn't work on a .22 chamber as well.
Take a wooden dowel rod that is undersize for the chambers. Cut a slit in the end of it, as deep as you want to enter the chambers to polish. Then, insert the end of a thin strip of 600 wet or dry paper into the slot, and wrap it around the dowel. Check the fit in the chambers, you want it snug but not tight. Then generously oil up the chambers and paper and either chuck the dowel rod in a hand held drill on low speed, or better yet, in a drill press on low speed. Run it for a minute or so, slightly moving it in and out a few millimeters so as not to stay in one place. Check your work, re-oil, and continue until you get the polish you want on the chamber.
[snip]
Lou