The Ugandan army didn't actually fight they just looted and fled. all the fighting on the ugandan side was done by the contingent of libyan troops sent by Qadhaffi, so either make Qaddaffi able to send more troops or have another country send troops to aid Idi Amin.
According to Wikipedia there was East German involvement with Idi Amin's regime, perhaps you could have East German troops disguised as Libyans fighting in Uganda.
I think that if it happened it would have disastrous consequences, NATO would probably see it as a communist plot to conquer East Africa.