Moi Airport in Mombasa uses 2 small terminals, which are connected in the public area by a short (about 50 metres) covered corridor.
The larger terminal serves all international flights and the smaller terminal (on the right when viewed from the outside) serves all domestic flights within Kenya.
The terminals are rather dated but very clear and the distances are small.
Queues for immigration or security checks are usually 20-30 minutes at most.
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Transfer between flights
Mombasa is not a typical transfer point, which is one of the reasons why the airport does not have direct transfer facilities.
You must always go through Kenyan immigration control, exit the transit area and check in again.
In any case, you will therefore need at least a Kenyan transit visa for 20 usd.