There are as many ways to clean an AR as their are AR experts, that means two for every serious shooter

. Seriously, I've seen high masters use opposing methods to the same end result. I've also talked with some of the industry's most respected experts and have seen opposing views. My conclusions is that it isn't a critical component to barrel life or even optimal accuracy. I've now had the opportunity to watch multiple barrels over their useful life and am comfortable with the methods I use.
I never put a brush down my bore, ever. I use patch out as a solvent, with patches only. And then I use JB to polish the throat gently every three to five hundred rounds. This has proven effective for me and given me great barrel life.
My actual process is to use patch out accelerator the first patch with a tight fitting piercing jag. Then I wait about five minutes and follow that with patches soaked with patch out for four to eight patches until it comes out light gray. Then I switch to dry patches until they come out white or very slightly grey.
Then I wait 20 minutes and go through with a wet patch again. If it shows blue I may pass several more wet patches until the blue goes away and then dry patches until they come out white.
This has proven god enough for me to consistently place in the top ten percent in national level competitions.
Bob