What is the chemistry of a black hole?
"Black Holes" are a physical phenomenon of gravitational forces. Elements exist within them, but they are not related to the formation or continuation of the phenomenon.
"Chemistry" itself is a very broad term, describing one of the physical science disciplines (like physics and astronomy). We may observe things that may give us some idea of the elements present in "black hole", but we have no direct measurements of any particular chemical processes that may go on within them.