I want to start up a Bitcoin exchange in Kampala Uganda but I want to first know what the law says on crypto currencies.
Bitcoin was "banned" in Kenya, probably because the central bank realized its growing popularity among the business "creme" and its eventual increase in value to where it is now. Technically, it is not illegal to use it but you can expect some resistance from government. Since Uganda is a neighbor, and probably thinks and acts along the same lines, my guess is that the crypto-currency will be banned there too if it hasn't already.
There is a Wikipedia article that tracks legality of Bitcoin in different countries. Unfortunately, there is no information added for Uganda, yet. Anyhow, I can only recommend that you get actual legal advice locally.