From page 2 of the Kenya Independence Act as linked below:
“(2) Save as provided by section 3 of this Act, any person who immediately before the appointed day is a citizen of the United Kingdom and Colonies shall on that day cease to be such a citizen if on that day he becomes a citizen of Kenya.”
The provision was altered in 1981 by the British Nationality Act of 1981, but those changes would not have affected Obama.
I am afraid this is empty, verbal talk, from people still unfamiliar with international law.
British law, not the Kenyan Constitution, determines who is or isn’t a British citizen: that is a consquence of British sovereignty (and I think the article I posted says something about that).