He renounced his citizenship in Kenya and Indonesia simply by not living in the country for a certain number of years.
Indonesia, from what I've read, does not allow dual citizenship so he would have had to formally reclaim his US citizenship on turning 18 IIRC. Apparently there was never a formal request to regain his US citizenship.
So apparently he isn't a citizen of any country.
At this point, from what is publically "known", Barry is an outright admitted multinational. He was born a, or has been a, British subject, a Kenyan citizen, possible U.S. citizen and possible Indonesian citizen.
It's a slap in the face to our framers to think they would have agreed that a multi-national was considered a natural born Citizen. The terms are mutually exclusive.