This seems to be a bit of an interesting one, as I got it after being set afire in 109 G-6 in a fight against a P-61. He put me afire, and I returned the complement. But I only killed him in that particular fight. (It was Sim Battles Enduring Confrontation, near the end of a two hour match. )
Now this was in Sim Battles, so it might be that the kill counts double there....or I might have killed someone else while on fire in that match, I'll have to review the replay.
Now the important thing about this achievement is that the other one dies either while you are on fire...or after you have died due to your aircraft being burnt down.
Incidently I got Vengeful Spirit for that same kill.