Travelers arriving in Kenya from any country with risk of yellow fever transmission are required to posses a valid vaccination certificate for yellow fever. Countries that fit this category include Zambia and Tanzania.
Travelers from a non-endemic country arriving directly to Kenya and back home (i.e. London – Nairobi – London) will not require a yellow fever certificate.
Those travelers leaving Kenya and continuing their travels to Tanzania (including Zanzibar), South Africa or Rwanda (and possibly other African countries, even if only for a transit) will need a yellow fever certificate to enter those countries.