Upvote:5
No. The airline will not hold luggage for you. Not voluntarily anyway. If you failed to pick up your luggage at the airport, they would probably hold if for a few days providing it didn't go missing. It's not a recommended strategy though.
Ideally you should look for a left luggage service at the airport or in the city. If you're staying at a hotel in Nairobi, it is often possible to leave luggage with them for little or no payment.