It's difficult to pinpoint an exact timeframe for the design process of the Kenyan flag. However, the documents I’ve linked to do provide a sense of the timeline and the various stages involved:
Early Design Discussions: The sources indicate that discussions about the design of the national flag were underway by June 1963 [ National Archives. The National Flag. Cabinet Minutes1 ]. There was a debate on whether to use gold or white to separate the major colours, with white being chosen
The size and design of the shield were also considered [ National Archives. The National Flag. Cabinet Minutes2 ].
Cabinet Involvement: The Cabinet was actively involved in the design process, reviewing various designs and providing feedback. They considered different sizes for the shield and debated the use of metallic gold versus yellow-gold.
Formal Approval: By October 30, 1963, formal approval had been obtained for the national flag of Kenya, and it had been returned to the College of Arms for registration [ Secretary of State for the Colonies, 19633 ]. This indicates that the design phase concluded before this date.
Production and Implementation: There were issues in November 1963 with the receipt of flags, suggesting that production began soon after formal approval of the design [Director, 19634 ].