Does Bolt work in Nairobi, Kampala and Dar es Salaam?

Yes — Bolt is well established in all three cities and is the easiest way to get around as a tourist. Nairobi also has Uber. Kampala has SafeBoda for motorbike taxis. Always confirm the price before you get in, especially in Dar. Get a local SIM on arrival so you're not relying on international data rates for the app.