All the major carriers and their partners provide daily service from major cities in the US to Africa with most flights having a stop in Europe or in the Middle East. There are only a few non-stop flights including South African Airways' daily service from New York (JFK) to Johannesburg (JNB), and from Washington DC (IAD) to Johannesburg (JNB). Delta Airlines also has a daily non-stop service from Atlanta (ATL) to Johannesburg (JNB).
We are able to recommend and help you book the appropriate international flights to the starting point of your safari in Africa that works best with the itinerary you have chosen.