Good find. There was an interior link for April 1960 air schedules. It gives times for London - Nairobi with several in between stops, none of which are Mombasa. There is no London - Mombasa listed. There is a page for “African Local service” which lists Mombasa on the Khartoum to Dar Es Salaam route.
I can't imagine flying that route today, much less 50 years ago.
RE flight schedules, why a flight from London? Besides the boat option, why not fly from Hawai’i around the other way, changing planes at other friendly places? [not sure of the max. long-haul flights at the time.]