Hi Alex
looks like you've got one of the best routes already - JFK to NBO and then NBO to JRO. There are flights to JRO from Entebbe, Uganda (EBB) or Kigali, Rwanda (KGL) on Rwandair Express. Rwandair also flies into NBO...might be worth a look. They codeshare with Kenya Airways.
You could fly into Entebbe on BA - but it could cost more than to NBO.
st