I have attempted to do a trace of your inquiry, but with limited success as far as direct results are concerned, I fear.
This is what I came up with after this entry into my Google engine:
produced a caption reading "Micromark Organisation & Order of Battle Charts":
which in turn produced these captions:
Napoleonic Armies First World War Armies Interwar Armies, 1924/39 Second World War Armies Post-1945 Armies.
When I entered the Second WW Armies section I found a caption:
African Forces AF-1 African Infantry Division, 11-40/11-41, East Africa AF-4 Kenyan Home Defence Force, 1939/40, East Africa.
It appears that descriptive booklets are available ( 0.80 pence plus postage each), but I haven't read through the entire 32 pages of this missive to determine where one addresses/remits in order to obtain this material.
No more than I know about it, I assume that your G/F may have been involved, at least marginally, with the establishment of the home defence force in Kenya.
This is about all I can accomplish for you on this end. I have five excellent military reference books, but can not come up with any reference to East Africa Engineers.
And I could find no reference to Field Coy nor to the 1st. African and 12th. African Divisions.
I do hope that this information is of interest and benefit to you and your family, and that it may in some way put you on the right track to finding these units.