When I clean a breech plug... I remove it from the rifle. I then place it normally in a soaking jar (old jewelery cleaning bottle with the lift up tray in it) which is filled with Rusty Duck Black Off or Simple Green. I change the solution out when it becomes filthy dirty.
As I clean the rifle, I finally come to needing to clean the breech plug. I have two brushes I use, and some Q tips. The first brush is a brass brush (used for cleaning battery terminals) and the other is a tooth brush. I use the brass brush to scrub the teflon tape off it and any hard to get fouling. I only scrub the plug in one direction through the threads. I never scrub with that brush. After the brass brush I use a soft tooth brush and finish cleaning all the hard to reach places. Sometimes a small dab of Soft Scrub is used it the plug is being difficult. I then take Q tips and work the whole plug over. When there is no fouling on the plug I pour some isopropyl alcohol through the flash channel and then shake it real hard to dry it. After that I apply the teflon tape and then a light coating of Slick 50 One Grease and immediately put it back in the rifle.
I have some real concerns with a powder (BlackHorn 209) that forces me to use a drill bit to clean the flash hole of my rifle. When I shot BlackHorn 209 I was not aware of any of this flash hole nonsense and ended up throwing away the breech plug from my Knight Disc. It was plugged, I soaked it in a number of different things and tried to blow it clean with a air compressor. I also tried to pick it clean but could not get it clean. I just figured it was from old age as the plug had hundreds of shots through it, and the face was showing wear long before I started shooting black horn 209.
After I ran out of BlackHorn 209 I went back to my other powders. Mostly black powder, Pyrodex and Triple Seven. Even and dirty as those powders are and crud rings they can create, I never had to take a drill bit to any of them to get them clean.