I agree that, unless fired brass is deformed, leave the chamber alone or send the rifle back to the factory for service.
If brass is slightly deformed by the scratches, I'd take a fired case, modify the base so it will take a screwdriver shaft chucked in a drill, coat the case with Flitz or JB Bore Paste, then rotate it slowly in the chamber with light force. Such polishing shouldn't be so aggressive as to change chamber dimensions.
In an older rifle whose chamber has rusted, a brass brush with 000 steel wool on a cleaning rod, turned by a drill works well. Too little polishing is better than too much!
People are like rifles. Some are tried and true, having great eyes, personality, and fun to be with. Others never seem to hit the mark with you. Still others go off half-cocked. Still, it's nice to know most of them.