Was Kenya ever a British Dominion? Answer -- YES.
From the official Parliament of Kenya web site:
The interim period of Internal Self-government, did not witness any major constitutional changes. The constitutional provisions finalized in February, 1963 remained virtually the same. At midnight on December 11, 1963 , Kenya regained Independence from the United Kingdom.
Kenya remained a dominion within the British Commonwealth , with a Governor-General representing Her Majesty locally and a Government headed by a Prime Minister. Mzee Jomo Kenyatta, leader of the majority party in Parliament, became the first Prime Minister, heading a cabinet of fifteen Ministers and thirteen Parliamentary Secretaries. The late Ronald Gideon Ngala, leader of K.A.D.U. and Mr. Paul Joseph Ngei, leader of A. P. P. formed a Coalition Opposition under leadership of the former.
The composition to the Legislature and the framework of the Government at Independence remained in place until the first anniversary. Arising from close negotiations between the Government and the Opposition, a merger of all the parties represented in the House, under the Kenya African National Union - K.A.N.U. and under the leadership of Mzee Jomo Kenyatta was concluded and took effect on December 12, 1964 with the voluntary dissolution of the Kenya African Democratic Union - K.A.D.U. and the African Peoples Party - A.P.P. This merger meant an unanticipated de facto one party status. On December 12, 1964 , Kenya declared herself a Sovereign Republic within the Commonwealth. Mzee Kenyatta become the first President, heading a Cabinet of eighteen Ministers.
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From the sound of this, it doesn't seem like in Feb 1964 that it was clear that a Republic was in the works, and extremely unlikely that forms would have been made up with the new name. More likely they would have continued with the old forms as more important things were going on.
Stamps in the Dominion period just said KENYA, Republic of Kenya Stamps were issued Dec 12, 1964.
ADDED: According to Kenya, colonial-era documents were marked "Colony and Protectorate of Kenya", while Republic-era are "Government of Kenya".