You know that boss enemy in a video game that you can't get past no matter how many sticky bombs or throwing knives you toss at it? It always finds a way to take your face and give it a nice little sitting area on it's mantle. That would be a flamethrowing atomic bomb. Sort of like the "Golden Egg" scenario.
A Flamethrowing Atomic Bomb is an impossible-to-defeat-without-sever-repercussions entity in a video game or in real life that, no matter how many solutions you may toss at it, turns out just won't go down without fucking other shit up.
In a video game scenario:
Average Guy 1: Oh, my god! I'm up to Level 22 with that one boss.
Average Guy 2: Ahh, that guy's a Flamethrowing Atomic Bomb.
AG1: WTF?! I got killed on the first shot?
AG2: Told you, my turn.
In a real life scenario:
Guy 1: God, Mr. Dink is a fucking flamethrowing atomic bomb.
Guy 2: Why's that?
G1: He wants me to complete all of these TPS Reports by Thursday but I already explained to him that's not my department!
G2: Huh..What does that have to do with a flamethrowing atomic bomb?