I have done much research but would appreciated any suggestions in doing JFK to NBI (Nairobi, Kenya) sometime in Sept or Oct 2014.\

I have
Chase Ultimate rewards 600K points
BA 100k miles
UA 125k miles
SPG 80K points
AA 600K miles

Spouse has
BA 125K miles
UA 160k miles

I also have access to an 100K additional AA miles in a relatives name.

I would need 2 tickets, BUSINESS or FIRST CLASS.

I would consider going via the Pacific if necessary, although I do not believe I can use AA miles to do that. Another problem with AA miles is the BA surcharge when going through London

I would also like to avoid Egypt Air since I have heard that neither their Business or First class has lie flat seating.

Specifically are there any connections through the middle east (other than Egypt air) that can be done on a mileage award.