If you want your barrels as clean as can be use a product called Wipe-Out. It comes as a foam cleaner or as a liquid. An accelerator is also sold than supposedly doubles the speed of the product. It is not cheap, but no other product cleans like this stuff. After letting the stuff sit in the barrel a day or two. Wipe it out. Your bore will be as clean as it was when made. It is not corrosive or harmful to stainless or carbon steels. Nor does it reek to high heavens. After you wipe it out. That is it. It prevents rusting.

Unlike some other cleaners, there are no corrosive or erosive elements to harm your bore.