Get some monofilament fishing line. The cheap stiff stuff.
Get or make some patches (old T-shirt material, etc.) and cut them in to approximately 1-2 inch squares.
Tie (simplest knot) several of the patches a few inches apart onto the monofilament fishing line.
Leave enough bare fishing line to thread it through the barrel and be able to tie it into a loop once threaded into the barrel.
Pull the patches through the barrel and if you have created the loop, you can pull the multiple patches through the barrel as many times as you want.
This is VERY simple and EASY to do, not to mention VERY, VERY CHEAP!
Any lb test fishing line will do as long as it is stiff enough to thread it through the barrel. I have used from 6 lb test to 20 lb test.
The cheaper/stiff line works best.