AFAIK, AA doesn't fly to Africa and One World is really weak there. You might have to keep connecting via LHR - that's when you wish you belonged to another alliance. Anyway, you can try to combine these airlines for the following legs-

ORD-DXB: AA, BA, RJ
DXB-NBO: BA, RJ, IB
NBO-ORD: AA, BA, IB

As pointed out above, it may be better to consider a OW award. And it may be advantageous to book before the new rules take effect.

Later edit: The following itinerary should be bookable on OW carriers. It will be under 20K miles (under old or new rules) and thus make a nice OW award (for business class, the relevant award is OW130C and will cost 130K miles, see http://www.aa.com/aa/pubcontent/en_U...s/oneWorld.jsp):

ord - lhr - dxb - amm - nbo - lhr/mad/amm - ord

The old/current rules only consider direct distances among cities you wanted to visit and skip the connecting ones; in this case it would be ord-dxb-nbo-ord (17,478 miles). The new rules will consider the actual distance flown,eg, ord-lhr-dxb-amm-nbo-amm-ord is 19,413 miles.