Go buy about 3 feet of clear silicon tubing, the interior diameter of which needs to be small enough to fit over the nipple.
Fill a small bucket with hot, soapy water. Take you cotton patch and wet it with the soapy water and insert the other end of the hose into the bucket. Take your cleaning rod, with cotton patch installed, and place that into the end of the barrel and commence to pump the water from the bucket into the barrel. I like to use a clear tube so I can see the soap co in and the gunk come out. After a few minutes of pumping, your barrel is clean. Run a few dry patches down the bore to remove and moisture and then oil the bore.
I would also purchase a breach face scraper to clean the face of the breach plug. The fouling can really get baked in, and all barrel cleaning your efforts may not dislodge it without using the scraper. They're available at "Track of the Wolf."
I've cleaned my musket 100's of times in this manner, and it cleans the bore better and faster than anything else I've tried. They even make a "C" clamp type of devise that also works for flintlocks, but you have to remove the lock first.