Fire escape ladder cannot be used if the floor (room) below is on fire?
This is why every livable room is required to have at least two ways to exit room.  If all paths are blocked, you then have to wait for the fire department to come with the ladder truck.  Any other means will put you in greater dander.

Also it is not the ladder catching on fire that is the concern, but climbing through heat/fire/smoke that will make it impossible.