The low fat people say no fat in their diet and no fat before a flush. The theory is not to stimulate any bile flow so that you build up pressure before the flush to maximize the effectiveness.
The high fat people say that you must eat sufficient fats daily in order to keep bile moving, including the day of the flush to help prime the pump. Dr. Kelly has a version of the flush where you eat whipped cream beforehand.
My personal opinion is that a certain amount of fat is proper for humans to eat... evidenced by the fact that we have lipase enzymes, and we have gallbladders which contract when stimulated by either bitters or fats, and a big part of the liver enzyme system revolves around lipids and lipid solubility.
You have to try both methods and see what works for you.
The first thing people should do when formulating a health plan is test macronutrients ratios- protein:fat:carbohyrate and see where you feel best.
I think genetics play a big part and people (with problems) skew toward one end or the other, so it's relatively simple to figure out which camp you belong to through experimentation. Also I think there is a relevant correlation between blood type and fat tolerance.
Blood type A has lower alkaline phosphatase and does not digest meat and saturated fat well in general, O and B do better with fats.