Good catch.....I found this which stated the 1963 Independence Constution only lasted a few months before being dismantled.
...”But Kenya’s Independence Constitution lasted only a few months in its original form: Kenya’s ruling elite, who has taken over from the departing colonial authorities, quickly dismantled the Independence Constitution and declared Kenya a Republic”
I know officially it was Dec 12 1964 but did they use Republic of Kenya in the interim?