Have you flown more than 6 or 7 hours at a stretch? Flights from New York to Hong Kong can be 16 hours long, non-stop. About the same for Mumbai. As for Nairobi, there are no none-stops, far as I know, so you're up for another nearly day-long trip.
I'm a pretty good sleeper on planes, so long as Ambien is at the ready. Despite Tiger Woods' reported use of Ambien for other purposes, my experience say it's a pretty sure-fire way to get into the snore zone fast. (But don't take your Ambien until you get on the plane. On a flight to Hong Kong, my husband took his pill while we were still in the airport lounge...and then the flight was delayed. When they finally announced departure, it took me and a burly volunteer to get him up on his feet and walking to the plane. He was, well, zonked. Needless to say, he now follows the "wait-'til-you're-on-the-plane-rule.)
That may get you to sleep, but jet lag once you arrive is an altogether other question. There are many theories out there, but the one I swear by when taking a flight of more than 3 hours difference in time zones, is to get myself into the time zone of my destination as soon as I can, preferably the day before I've even gotten on the plane.
This is not easy to do in the practical workday world. It works best when you are taking a daytime flight (night time in your destination city) and able to take Ambien as soon as you get on the plane, treating it as your night time. If you're going to Hong Kong, for example, and can get a flight that departs at 11 AM from JFK, you're in good shape. You sleep 7 hours on the plane (no eating, no watching TV...this is bedtime), then force yourself to wake up and treat the rest of the flight as your daytime. It works even better if you've been following this clock for the day before you leave. This means--yes, grit your teeth--that you've stayed up the night before, all-nighter style. This is a great time to catch up on movies you've wanted to watch, books you've wanted to read, sometimes even work you've wanted to do. And if you prevail (the last few hours are the toughest), you're ready to sleep when you get on the plane and you're in great shape by the time you reach Asia
This works best if you have someone willing to talk with you during your all nighter. This is where you find out who your true friends are, right? Although I have some friends who normally don't go to bed until 1 AM or so, that group thins to zero when it gets past, say, 2 in the morning. And that's the tough part of the ritual. So my plan is to alert friends of mine who live half way round the world and enlist them to help me. It goes something like this: "I'm flying to Hong Kong tomorrow and doing that all nighter thing again. Would you call me at 2 PM your time? That's just when I'll be getting tempted to give up on the plan and crawl under the covers." I ask someone else to call at 3 AM New York time, and someone else for 4 AM and so on.
As I say, this is a test of friendship. If you've got stalwart types who agree to phone you (and further agree they won't tell you all the reasons it's a stupid idea) you can make it work. I'd be too embarrassed, after enlisting my friends' help, to have them call and find me asleep. So this gives that added shame aspect to the whole undertaking. And it's a great way for me to catch up on what they're up to.
So why not just set the alarm clock for every hour? Or employ some other trick to distract yourself? Easy. In the end, it's always conversation that keeps me going, makes me curious, makes me think and thus keeps me awake. So the next time you're planning a long flight, put on your checklist the important item of enrolling your friends in assisting your all nighter. You may even remember what you said while you're jabbering away with half closed eyes.
And if you don't have friends who live half way round the world, make it part of your plan to make some friends when you're there. And warn them they'll here from you when you're planning your return trip.