Travelling to Uganda from Capetown

pretty darn far, i reckon its about 5,500km.... give yourself a couple of weeks minimum unless you just want to rush it and get straight there, i think then you could do it in three days (uganda, tanzania, zambia, zimbabwe, SA) provided you never stopped or slowed down, which won't happen!

Is there a special reason to drive there? If not a flight will be a lot easier and cheaper.

Driving would take probably 8 days of just driving (and stopping at night) - if you have a month to do it then great, plenty to see along the way, but if it's just a transit it's not a nice trip.