I hesitate to give health advice because I'm no expert.
I can share that I've done Liver Flushes together with fasting and can't think of a reason why a fruitairian shouldn't do them. The main thing is to read, read, read and educate yourself before trying it.
Some people have concerns about stones getting stuck while flushing. It's something to be aware of.
High quality virgin olive oil is "good oil" and it would only be taken in high quantity for a short time.
The main thing I think is important is to take herbal dewormer and herbs for keeping wastes moving out of the body for at least a week or two before liver flushing.