Some major airlines -- like Delta or Lufthansa -- will fly into one or more major cities in the country where you're headed, but once you're in Africa, you may need to take a local airline to reach your final destination. If you're having trouble finding an airline that will fly you into your destination in Africa, you might check out South African Airways.
When you're packing for safari, you need to take your luggage weight into account. Because many safaris require you to not only fly on major airlines but also on smaller carriers, there may be different weight requirements. You'll want to check with the tour company you're using and with all of the airlines you're flying and pack for the lightest requirement. For example, Eyes on Africa restricts your luggage weight – including cameras and your carry-on bag – to between 26.4 pounds (12 kilograms) and 44 pounds (20 kilograms) depending on where in Africa you'll be traveling with them.
Also you may not be able to bring wheeled luggage. Some smaller aircraft require that everything must be packed in soft duffel bags.