Uhuru Day:
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.
The Kenyan site is not real clear, but it sounds like Kenya already had their Constitution in-place, when they declared their independence. Their Constitution is a Republic form of government.
It took India 3 years to come up with their Constitution after independence, but Kenya already had a Constitution.
“India attained freedom on 15th August 1947. Our National leaders set up the Constituent Assembly to draw a Constitution for India. Our constitution came into force on 26th January 1950, we celebrate this day as the Republic day.”
It does say on the Kenyan site that
Bicameralism
“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. December 12, has since been celebrated as Jamhuri Day. The first Vice President, Mr. Jaramogi Oginga Odinga, resigned on April 14, 1966 and immediately formed an opposition party, the Kenya Peoples’ Union - K.P.U. This reintroduced a dejure multi-party status. The late Mr. Joseph Anthony Zusarte Murumbi, hitherto, Minister for Foreign Affairs was appointed the Vice President on May 03, 1966. “
So the site itself isn't clear when it became a Republic — at Independence 1963 or a Sovereign Republic in 1964.
If it was independent in 63 and they already had a Constitution it sounds like it became a Republic in 63, but maybe not a Sovereign Republic until 64.
Real or not, I’m learning a crapload about Kenya.