In the shop there is normally a 5/32" drill chucked in a drill motor, close to where i clean the rifles. What i do is remove the vent liner, and run the 5/32" drill all the way through the breech plug, from the primer end. Most of the flame channel is not threaded, and seems to guide the drill past the threads so that neither the threads nor the drill 'knows' the other is there.
After the breech plug is soaked, and wiped off, the vent liner has always been re-installed, without an issue. Never once have i damaged threads using the described method. However, if somehow the threads were damaged, it would be a trivial matter to 'chase' the threads with a 10-32 tap. At least i think it would be trivially easy, but cannot say for sure, because i have never done it.
The flame channel could probably be cleaned with the vent liner in place with no problem, but i have never done so. Myself, i don't think it matters how one goes about removing the carbon from the flame channel.