9 months, 12,000km
At present this would probably be ill-advised because of the political situation in Egypt.
It can be done by an organized tour called Tour d’Afrique. Their route is 11693 km, they leave Jan 14th and arrive in Capetown May 11th, the cost is 9,400 Euro. This is a supported ride, and personally I would be using the sag truck rather often as average day rides are in the 106-154 km range. If one does a little research on Tour d’Afrique on the internet, one thing to be found in almost every blog is the EFI (Every Fabulous Inch) status. Apparently only about 20% of the riders are actually able to make it all the way to Cape Town without ever having to ride in the sag truck.
I would prefer to stop and smell the roses, so rather than the 4 months the Tour d’Afrique takes I propose 9 months, leaving the Tour d’Afrique for the super athletes.