I did a flush using sesame oil which worked great. And tasted pretty good too. After a dozen flushes you get to where you dread the thought of all that olive oil, even though you love it on salad.
Coconut oil is thought to be processed differently by the liver and doesn't work very well for liver flushing. I've heard of a couple of people having success with it but that's only a very few in three years of reading curezone. I've never tried it because if I'm going to go to all the trouble of flushing I want it to be worthwhile.
But like the other poster said, coconut oil is really good stuff otherwise.