Why are flights in Africa so expensive?

Part of the reason is the lack of competition on so many routes, because countries restrict the rights of airlines from third countries to connect them with other countries - so called "fifth freedom" rights - despite an agreement to do this in 1999.

A comprehensive 2010 World Bank study led by Charles Schlumberger looked at a number of specific examples of what happened when routes have been liberalized in Africa. When the Nairobi-Johannesburg route was fully opened up in 2003, passenger volumes increased 69-fold. When the domestic South African market was liberalized, passenger volumes increased by 80 per cent. On average in the Southern African Development Community (SADC), routes that were liberalized saw fares drop by 18 per cent. The study estimates that full liberalization in the Southern African Development Community (SADC) region would increase passenger volumes by around 20 per cent.

More here (by me) on the AfDB Integrating Africa blog.