I'm not the most experienced person here, but I think you should break the fast according to the book, before you attempt a liver flush. Not doing so can make you very ill. The oil drink is very heavy to digest and it's a shock to the system when you haven't eaten in a long time.
Some people have gotten great flushes on the fast, others ended up feeling ill and throwing up. Is it worth the risk?
Read old posts about this and then make an informed decision.
Best of luck to you!