How can my wife work when I relocate to Nairobi

Hi, There are lots of posts on this subject.

Unfortunately your wife would need to have a job offer and relevant work permit to be able to work in Kenya, either in a paid or voluntary capacity.  This would have to be obtained prior to travel. 

Generally speaking, spouses and children obtain a Dependent Pass to enable them to live with you in Kenya.  However, this prohibits any paid or voluntary work.

With regard to starting a business.  it is relatively easy to register a company, but an entirely different prospect if your wife wanted to run it.  For that she would need a Class G Permit and to obtain that you must have a minimum of $100,000 capital.  This requirement is extremely frustrating, but exists to encourage foreign investors and to support small businesses being run by Kenyans.

Kenya is not the best place to be if you fall short of cash, so I think that you need to plan and think very carefully.  As you haven't stated your salary and any benefits (housing, healthcare, transport), it's difficult to assist any further. 

As an aside, I was offered a social enterprise type position in Tanzania years ago, but sadly had to turn it down, as the income would have been too little to support my family.  It was an incredibly hard decision to make, but the correct one, in retrospect.