Hi David,
You dont say which tki that you will be taking?
With nilotinib you will need to fast but with the others you might find that taking the pill with a substantial meal and a few glasses of water could be crucial as otherwise you might suffer from nausea and also headaches/dizziness.I have been on imatinib for 15 years and still sometimes dont get it right.
I suggest you experiment with foods that help you to absorb the pill without nasty headaches and nausea etc-go for high carb stuff like pasta or a substantial sandwich or full meal .I suggest please(except nilotinib) dont take on an empty stomach especially with imatinib.
Re supplements -have you had your Vit D checked and if needed take it with Vit K:taking it wont harm you anyway nor will the sun in moderation.
So in summary when you start your tki I suggest that you experiment and then find the best foods for you in combination with the tki and the right meal and time of day and keep hydrated with lots of water.
Lots of good luck
John