Without the Pyromaniac perk and Broken Steel DLC, this is the most powerful flamer. It's found in the Franklin Metro utility along with plenty of flamer fuel. It is not affected by the Pyromaniac perk, essentially being a flamer that automatically bestows the perk on you while using it.
Burnmaster can shoot a total of about 139 units of flamer fuel, the equivalent of 3 reloads, from full condition before breaking.
When you have managed to find Franklin Metro Utility in Falls Church/Mason Dst Metro (it's all the way in the back, down the tracks past the mezzanine), follow that until you get to where the tunnel goes down into the water. Go into the water and then make a left through a broken passage in the tunnel (if you do not have a radiation suit, carry on past the broken passage and keep going straight down into the water, there is a box with a mini nuke on top and in the box is a radiation suit). Swim to the right until you find a ramp that goes up. Continue down a hallway filled with radioactive barrels. It's advised to bring along a bottle of Rad-X, some RadAway packs, or a radiation suit, as the area has moderately high levels of radiation along with numerous glowing ones. At the end of the tunnel are five ammunition boxes filled with flamer ammunition and the Burnmaster.
The Burnmaster does not benefit from the Pyromaniac perk, and it does the same damage as a regular flamer if you have the perk. The Unofficial Fallout 3 Patch fixes this bug, among others.