I just did a very productive Liver-Flush on Day One of the ten dayer I am on, and followed it up with a pro colonic Monday morning. Soon I shall have sunshine coming out all my orifices!
I think it is a personal choice whether or not to do a Liver-Flush in conjunction with the MC. It's a good time because presumably you have done a little pre-fast cleansing, tapered off coffee, eaten clean for a couple days etc. ... and the first day of the fast you haven't eaten anything, and you would need to quit eating early the day of the Liver-Flush anyhow... so you're kind of naturally prepared.
So if you choose to do one, great! Certainly it isn't a requirement of any sort. Just a nice do-dad.