For some fast, not too thorough, cleaning I use felt pellets. 1 felt pellet soaked in ballistol followed by one dry felt pellet and that followed by a lead pellet. I can do this because i have more than enough space in the breech, in an AA this is going to be hard I think..
For thorough cleaning I take out my barrel and use a cleaning rod, first calmly with a brass brush, than thoroughly with a nylon brush and finish the cleaning with a woolen brush. During the brushing I spray some ballistol in the tip of the barrel. After this, the barrel is so clean that the first shot is around 250 fps slower than the normal muzzle velocity. After this type of cleaning it takes a couple of shots before the accuracy is back at its normal level