Our first trip to Africa with a baby was to Arusha, Tanzania when the older boy was just one. Because we were planning to go into the bush we got our shots, and had our pediatrician suggest the correct shots for the baby given his age and where we were going. Our town also has a dedicated Travel Clinic that is a great resource if you're heading anywhere off the beaten path (anywhere without an airport nearby, for example).
This trip, the older boy is 3 and the new baby just turned one. The flights on the way here were a short one hour hop to Seattle, followed by a 10 hour flight to Amsterdam, then an 11 hour flight to Johannesburg. There were layovers between them, as well. Total wheels-up, wheels-down flight time was about 22 hours, but door to door time was about 30 hours total. Here's a few of the techniques that we've used/developed to make it possible.
All this added up to a difficult, but not nightmarish or oppressive flight. Both boys did famously and are having a blast so far. I'd encourage you do try these tips (tweaking for your kids' personalities, of course) and get your kids of their home country and show them the world.
Scott Hanselman is a former professor, former Chief Architect in finance, now speaker, consultant, father, diabetic, and Microsoft employee. I am a failed stand-up comic, a cornrower, and a book author.
Disclaimer: The opinions expressed herein are my own personal opinions and do not represent my employer's view in any way.