It depends

Ice vs Fire, ^ answer of Bruno Mars.

It depends (Simon can't go absolute zero, and FP can't make WHITE flames, which is the fuckin' hottest flame of all but we can't see the last three colors [eyes can only see the spectrum of the prism, not UV and radiation] and it looks like only white. WIZARD TALK :/)

Flames princess will win cause she is flames and ice king is a ice and flames princess can melt ice king

Flame princess because all she has to do is knock the crown off his head and then he will be powerless.

Ice only needs the molecules of a liquid in low temperature that it will stop moving (freezing) but fire needs a triangle.
Turn the triangle to a pair of parallel lines, extinguished.
Especially when Finn can help Simon turn heeyoomungus amounts of ice to water.

Naturally. Without IK's crown, he's powerless. Flame Princess can just burn him and if it gets to extreme she can just turn into her monster form.

But if there was water... ya know who would have advantages

I think of an another way:
We assume that Ice King froze Flame Princess, but she's made of fire, so it's not strange that she could melt the ice easily. But when ice is melted, it turns into water, and imagine that all that water falls on her...
It still depends though. Flame Princess could be faster and she could just knock the crown off.
And @marcelinerocker:
You should say: "Flame Princess can melt ice". It's not that Ice King is completely made of ice like Flame Princess made of flame! He still has skin and stuff you know! Using "melt" is kind of... inappropriate. You should have used "burn".

Nah, i think she used the right word. Cause that just show how real cruel FP can be. >:D

@makemesmile
Assuming that a wind carries her near the crown or Finn intervenes and takes it off for her.
Plus, Simon has no more ordinary human skin, remember?

I could have used Mystic Stasis ._. (RotMG, deal with it)