As long as the gun has been blued during manufacturing, or hot-blued. This type of bluing is actually made part of the metal. Flitz will clean and protect the barrel inside and out without any oily film or danger to the inside of the barrel.
If the gun has been cold-blued, then the bluing has been painted on. Flitz will treat this like graffiti and clean it off of the surface of the barrel. Check with a qualified gunsmith to be sure.