For the dragon stone, there is no cooldown if you teleport to the battle tower or between platforms, but when you leave the battle tower, at least in D2:ED there was something like a 5 second cooldown before you could teleport again.
I don't think there was a cooldown on the dragon morph stone. IIRC I accidentally transformed in one of the flying fortresses and was able to transform back before dying (once I did that and did die, but I think that was due to flying low and having less time to react).
