Chamber polishing is normally a final step in chambering a barrel and before tightening it onto the receiver.
It is best done on a lathe, using a cartridge case-shaped split mandrel holding strips of very fine (400-600 grit) abrasive cloth and finally crocus cloth.
The object is to POLISH only enough to remove the very fine tool marks left by a good chambering job. It must be carefully done to avoid enlarging or egg-shaping the chamber or neck. Several seconds of misguided enthusiasm is all that is needed to ruin the chamber. Keep the mandrel moving in and out and avoid enlarging the chamber.
With a break-open action or a barrel that is already fitted with lugs and can not be conveniently chucked in a lathe, it is possible to polish using a hand-held electric drill motor or pneumatic motor. The application is the same: very fine abrasive cloth on a mandrel and carefully applied. Avoid polishing the neck and throat areas and avoid enlarging the chamber.
After polishing, THOUGHLY wash and rinse the chamber and bore using mineral spirits, then warm soap and water, and finally, clean with solvent and oil. ANY grit or residue will ruin the bore on firing.
HTH
John