Using a drill bit will work but will eventually ruin your breech plug.
Thompson Center makes a kit for it that works better than the drill bit
Its a breech brush and fire channel breech brush combo kit.
I bought mine on Amazon for 6 bucks a couple months ago. I could not believe
how much carbon I scraped out of the flash channel on the breech plug. Right now they are out of stock
except for the 3rd party sellers that want 3 times as much for it. Wait till they come back in stock for 6 bucks.
Its called a Thompson Center 9508 breech plug and fire channel cleaning brush kit.
I use a can of compressed air to blow out the scraped off carbon while brushing
I also liked the idea on another thread by a member here that used a steam cleaner to blow out the flash channel.