Delta/KLM is our current preferred carrier from the USA to Entebbe, Uganda, via Amsterdam. Arrival and departure times for Entebbe are excellent, and layovers in Amsterdam either minimal or reasonable, and the airport has many amenities including a mini art gallery and tables with power supply.
British Airways allows 3 checked bags under its humanitarian fare, which is a great help getting items to the field. Their fares generally do not fluctuate very much seasonally, as other airlines do, so this has an advantage during summer flights to Africa, which is the high season. It's often possible to avoid overnights in London. And they have a good Starbucks at Heathrow.
Check with Delta concerning size and weight regulations and possible charges. Typically we're allowed a maximum of two bags not exceeding 50 lbs., with bags of combined dimensions of 62 inches. Team members are responsible for baggage expenses. Carry-on bag dimensions should not exceed 45 inches. Team members are responsible for possible baggage charges.