How to make a second story floor fire proof?
You can install cement board on the subfloor and then any flooring you'd like on top of that.  The cement board isn't that thick and is typically used to firm up the floor before installing tile, but you could put whatever you like on top.

However, rather than making the place only able to contain the fire, I'd consider installing sprinkler heads in the room to put out any fires before they have a chance to spread.