It is strictly up to the entity paying for the study. Typically, for government or public utility work, a P.E. would be required. But for a private company, it's between them and their insurance company. I've seen a lot of studies done in-house by plant EEs. There is no special certification for doing arc-flash studies.
"An 'expert' is someone who has made every possible mistake in a very narrow field of study." -- Edward Teller