Another ^ for KQ, flown l/h and s/h with them although never EBB-NBO. Can you get an Emirates flight between the 2, I know the DXB-EBB flight stops in NBO both ways, perhaps you can use them. It's only an hour or so iirc.

As for the drive from Kampala to EBB, that's probably the most dangerous part of the journey, those local buses can be crazy.

If you get a chance to use the lounge at EBB it's like stepping back in time.....

Safe trip!

Rich