I smoothed the outer surface of the ocarina in Blender's sculpt mode, while leaving the inner surface and all the holes untouched. This means that it will work just as well as the original one while looking a bit nicer. The smoothing gave it a bit of an uneven look whitch reminded me of an actual clay ocarina.
I decided to add my own Blender files as well, for anyone who wants to do further modifications. It is also subdividable now.
Only use supports touching build plate, make sure there are no inernal supports.