In theory, milk kefir will be entirely lactose-free (carb-free) if allowed to ferment for a sufficiently long period. I suspect that if allowed to ferment for 3 days, then 99% of the lactose will have been consumed by the kefir grains. As such, lactose-free kefir should be 99% safe on a candida diet.
I'm still experimenting with coconut milk kefir, but I suspect that the caprylic acid in the coconut milk will impair a majority of the kefir's probiotic qualities. But I'm not certain.
The bottom line:
1. Lactose-free kefir is fine on a candida diet;
2. The probiotic value of coconut milk kefir remains unclear and uncertain;
3. As a good compromise, I would suggest consuming BOTH milk kefir (lactose-free) and coconut milk kefir ... since the two are not mutually exclusive.