You need to a Kenyan national with a Kenyan CPL/Multi/IR. Their hiring seems erratic at best...in some years they will hire upto 12 new pilots and in the following year 4. The requirements have also been changing, sometimes 250hrs then 1000hrs minimum the next year. The age limit would also vary from a maximum of 35 yrs in one recruitment to 45years at the next. You get the picture.
They also require that you have a minimum B+ in Maths, Physics, Chemistry and English if I recall right, in the Kenya Certificate of Secondary School Education exam (KCSE) with a minimum aggregate score of B+ overall. The same score is the minimum score that would get one admission into any of the State universities.
If you meet the above requirements you may go ahead and apply to them, check their website
www.Kenya-airways.com under careers section. They will then invite you for an interview with the Chief pilot, 737 Fleet Manager and a rep from Personnel usually the HR Director herself. Here its to get to know the person behind the CV and the usual Perf A, Gas turbine and Airlaw questions will be thrown at you. If you answer them to their satisfaction, you will be called for a second interview which is an aptitude test, followed by a psycometric test, a medical test and finally a flight test in a Seneca or Baron shooting a few approaches at Jomo.
After which you will have your conditional offer of employment as a First Officer on the 737-300 subject to you passing the 737 ground school and thereafter about a months Sim Training in the 733 in London. Then ofcourse you will have to pass the base check, line check etc to be confirmed as a 733 F/O. The whole process takes about 6mths.
They have now started their own abnitio pilot training and the first batch of 15 are already back in the country from the Ethiopian flight school in Addis doing their conversions. The next batch of 15 is expected at the end of the year from South Africa. Maybe this is why they have kinda slowed down on hiring.
I have heard of some pilots who trained at Oxford there. There is also a number from Embry and other US universities and flight schools, South African trained, locally trained and ofcourse from the Airforce.
If you go to the Africa section under pay conditions thread you will find a poster by the name Kichwa Tembo who I believe is a KQ pilot. He/she should be able to give you more accurate pointers.
Good luck!