If you download it the document clearly states that anyone born after December 12th, 1963 would be a citizen of the Republic of Kenya. It is possible that it was not ratified until December 1964 but they operated under that name.
In any case, I think this document has enough identifiers in it as to be authenticatable or debunkable.
http://www.constitutionnet.org/en/vl/constitution-republic-kenya-1963-amended-2008
http://www.constitutionnet.org/files/Kenyan%20constitution%20amended%202008.pdf
THE CONSTITUTION OF THE REPUBLIC OF KENYA, 1963
(as Amended to 2008)
CHAPTER I
The Republic of Kenya
1. Declaration of Republic.
Kenya is a sovereign Republic.
++++++++++++++
I’ve written elsewhere that what matters is not what Media Matters quotes the WaPo as saying about Kenya joining as a “Republic of the British Commonwealth” in 12-1964 [http://mediamatters.org/blog/200908030001], but how Kenya and its government, since its indepedence in 12-1963 referred to itself.
This document reference found by politicalmerc seems to clear that little diddy right up.