I've never done a Liver Flush but I know a lot of folks here swear by it.
You should definitely use fresh squeezed orange juice- the bottled and canned stuff has lots of additives and just tastes awful. It will taste even worse than it usually does if it is the first thing you drink after your MC. I was on the road once for my job when I was breaking a MC, and I ran out of the fresh squeezed OJ that I had brought, and in desperation I stopped and got some bottled Tropicana. That stuff tasted just like a mouthful of chemicals...I couldn't even finish it and just drank water until I got home.