[Bozos of Bones]

Once you reach the top of the flames, when you see no more flames above, that is where the stone is. It is within the flames, a black orb. Walk up to it and use it.
If you are having trouble finding the room, just go back to the main tower and go up, left, right, through doors and areas, but never down. Once you use the Stone, it's stats will be randomly determined and it will be placed in your inventory. You will be teleported outside the gate, and the gate will be closed. This is not the end of the quest.