I found this achievement easiest to unlock on the map Highway. There is a flamethrower in the center of the map at the bottom of, and inbetween 2 staircases. (There is also a flamethrower on Waystation.)
Have a friend handy and load up wave 10 on Casual. ( the bloodmounts spawn like crazy on wave 10)Have your friend play defence for you and its usually wise to shoot the blood mount once or twice with your shotgun first to conserve ammo. You should get anywhere from 6-10 kills this way.
Note: the Flamer is on rotation with the Boomshot on Highway, and with the Mulcher on Waystation. So if you dont find the Flamer just let yourself die and restart the map.