Birchwood Casey markets a hot browning solution they call Plum Brown. I have browned a barrel in 2 hours with this product. It is super critical that you get the barrel absolutley clean and oil-free before browning. Use lacquer thinner in great abundance! I use a propane torch played up and down the barrel applying the solution once the barrel is hot enough to make water sizzle - no hotter as any hotter just means blotchy color. I generally apply solution to about a 12 inch length of one flat, rotate to the next flat and reheat and apply agent to the next flat, overlappin onto the first, rotate one more flat, reheat and apply agent to that flat overlappin onto the previous, rotate...etc. When I get to the next 12 inch segement I make sure I overlap tha heat and the agent so I get a smooth even color. My ususal method involves applying the browning one day, cleaning and carding a letting the barrel sit over night and then rebrowning the next day. I have gotten good results with this product but there is a bit of an "art" to using it.
Best Regards,
JMC
That is the only quick way to brown a barrel that I know of.