From the UK border agency
It was a British colony at the time of his birth, correct?
Note on Mombasa: Some have suggested that Mombasa was not part of Kenya until 1963, but I don’t think this is accurate. The British recognized Zanzibar as the legitimate ruler of pretty much all of the East African Indian Ocean Coast in 1895, including Dar es Salam and “Kenya.”
Relations between the Brits and Zanzibaris deteriorated rapidly, with the Brits going to war within a few years (Anglo-Zanzibar War, 38 minutes in length!). Slavery was a big issue, and the Brits basically seized and truncated Zanzibar at the very end of the 1800’s, the old Sultan was not permitted to return to Zanzibar, but was allowed to live in exile in Mombasa.