This achievement description is quite misleading. I just unlocked it after some trial and error and the only thing that finally caused it to pop was being burned to death by a flamethrower
I had 3-5 molotovs thrown at me and died at least two of those times from sitting in the flames and the achievement didn't pop. I also had a flamethrower sprayed at me but didn't die on at least two occasions and it didn't unlock either. I never encountered an enemy flare so I cannot say if that will or will not make the achievement pop, but the safest and most certain route would definitely be to die to a flamethrower
UPDATE: It's been confirmed from other gamers that you cannot boost this from teammates molotovs or flamethrowers. You must die from an enemy flamethrower.
UPDATE #2: The flamethrower was buffed several weeks after the DLC released and now instantly kills you instead of damaging you over time