In the thread Oldest music there is already a bit of discussion of very old instruments. Other remarks have been scattered in many threads. Since I have not found a thread only for very old instruments I start this new thread.

This link goes to a German article (I hope that link works for you, maybe I have here free access and you haven't)
about a very old flute made from a (part of a) mammoth tooth and dated by two different methods at an age of 35,000 to 37,000 years. It has been found recently in Suebia (?), Germany (in a cave with other, slightly younger flutes). Even if you can't read German that page has a picture of the flute.

Wolfgang