Yes. Ephialtes' v8 flamethrower made you emit a "Napalm" fire (like the Vehicle fire or larger Fire A emitter) followed by the standard "Burn" one after a few seconds. But that was all just an effect, it didn't damage you.
I think Rotondo had something in an unreleased version of Zombies (like, after the last v8 one but never added to v9's) where a burning zombie would light others on fire and damage them. It was in a video.