Actually there are different schools of thought here. I have read it recommended that a person can do a Liver Flush while fasting and I have done it while fasting.
I usually like to wait about a week after fasting to do one and digestion is back to normal I don't do The Clark Flush . I do one that is easier and more gentle on the system. I, too, question dumping fat into a system that needs to get up and running before digesting anything fat.
By 'ending the fast with a liver flush' I mean whenever you want to do it - it's good because fasting causes stones to form. My sis got gallbladder stones
by fasting and forgetting to do liver flushes.