Oh, sorry, I'm not familiar with the high fat candida diet.
I'm familiar with the MEVY diet (Meat, Eggs, Vegetables & Yogurt), but that's not high fat. Vegetables and LowFat or NonFat Plain yogurt certainly aren't high fat. Eggs have 5g of fat each, which is only 8% of the RDA, so 3 eggs would give you about 1/4 of the fat that the body needs daily. A large piece of grilled chicken breast without skin has 6 grams of fat. So you would have to eat 6 eggs and 5 large chicken breasts per day, just to meet the minimum.
The idea behind the MEVY diet is to eliminate sugar, grains, gluten and high glycemic index carbs to "starve" and displace the candida.
I've also heard of the Atkins diet, but that's not for Candida sufferers.
I googled high fat candida diet and couldn't find one.
Rebalancing intestinal flora and eliminating the candida overgrowth is about boosting the immune system. That is the goal. Candida sufferers have weak immune systems, and ususally suffer from some kind of autoimmune disorder. If the immune system fuctions properly, the body should take care of the rest. If cleansing (bowel or liver), water fasting, juice fasting, exercise, etc. boosts the immune system, then those should be considered possible paths to a cure.
I don't see where most candida sufferers on this forum are on high fat diets. I especially haven't seen anyone on a deliberate high fat diet that's also doing Liver Flushes and wondering why they don't work.