I agree with RalEva concerning your budget. Your time of departure is good as far as weather goes. In 2000 I did London-Capetown via the West Coast, and back to London via the East Coast in less than 5 months (see my book in the Books section).
Both coasts can be problematic. In my opinion, the West Coast may turn out to be the easiest. You should not have problems getting visas as far as Congo (Brazzaville). For Angola try their embassy in Libreville, Gabon. If you're not successful, you can airlift bike from Libreville to Johannesburg on their weekly jumbo. Shouldn't be too expensive. On the other side, Sudan is the problem. But if you don't get visa for Sudan, you can airlift bike from Cairo to Addis Ababa, and continue south. Plan C: You should be able to get visas as far for Chad, and if Sudan is impossible, airlift bike from N'Djamena to Nairobi. The important thing is, be flexible and bring money.