The fastest, easiest, and safest for the gun method to clean the chambers of carbon or leading is to buy a couple of bronze chamber brushes from Brownell's.
These are not only over-sized, they're made of a much stiffer bristle that cleans most chambers in one or two passes with no scrubbing, no chemicals, no soaking, no waiting, and no electric drills:
BRONZE RIFLE/PISTOL CHAMBER BRUSHES | Brownells
To clean leading from the bore, the above mentioned Lewis Lead Remover is fast and safe.
In addition, it's the only way to really clean the critical forcing cone in the rear of the barrel.
Use the forcing cone cleaning tip even if you don't shoot lead bullets. It also cleans off carbon and copper jacket fouling.
All the old time revolver shooters had a Lewis kit.
Hydrogen peroxide and vinegar will destroy bluing and can seriously damage guns. It also combines with lead to make a very hazardous chemical that can damage YOU.