Is skim/fat-free milk ok the day of flush?

I was wondering if having fat free milk the day of the flush is ok or not? I had my cup of coffee (which I usually drink with cream but substituted that for skim milk, don't like coffee black) in the morning, and I would like to do that again when I flush again. I know coffee is not the best thing but my diet is really good and I feel like I do well with one cup a day. I could skip it the day of the flush if I have to, but if skim milk is OK I'd love to keep it as it makes my morning a bit more pleasant (it's a ritual for me). My flush went well, but I still wonder if having any protein is counterproductive (Dr. Clark says no fat, but she also mentions no protein, but isn't bile only used when fats are ingested?).