Thanks for your service. I am an Iraq war veteran also and was there in 05.
Your cleaning method is an old trick that the Russians came up with to clean their AK barrels. They tied a few knots in a boot lace, dipped it in solvent and pulled it through a few times.
That being said, brass brushes and rods will not damage anything. Brass is much softer than the steel of the barrel and it is being pushed through very slow with solvent or oil on it. Think about this: every time you fire a live round, you are slamming a bone dry, extremely tight fitting brass bullet down the barrel at over 3,000 feet per second and that takes thousands upon thousands of rounds to wear out the barrel.
Pushing a wet brass brush on the end of a brass rod at less than 1 foot per second isn't going to damage anything, ever.