Spinning a round part in a lathe is probably the easiest way to polish it.
To start, we'll be using a metal lathe to speed up the process with a little tape on the threads to protect them. The 3-jaw chuck will hold the barrel securely.
We're starting with some 220-grit cloth-backed abrasive. Holding the abrasive strip around the barrel, move it back and forth the length of the barrel to get a smooth, even polish. Change to a finer grit to get the desired look.
For a nice matte finish, oil up the barrel and burnish the surface using a fine wire wheel.
Metal polishing is a little bit of art and a little bit of science; good metal polishing is a joy to behold.
-- Larry Potterfield