No, 12ga is way over sized. Also when using a bronze brush, never change directions midway thru. Push all the way out the barrel and then all the way out the breech plug. I hear some guys using a brush in between shots, but I high discourage it. Yes, you are changing direction where the powder sits, but I don't want any pits in my barrel.

Now I do use a 16ga brush to clean out my area where my breech is.