Milk thistle should probably be mandatory for parasite cleansing and with any liver concerns at all.
I would not do Liver Flushes while doing parasite cleansing. They could make you very sick. Happened to me and others.
There is no need to give up meat. In fact parasite cleansing can stress the adrenals and protein helps the adrenals a lot. Also a high quality vitamin C product like rosehips powder can stengthen the adrenals.
There is nothing you need to give up food wise to kill parasites though as always it is best to eat organic and avoid processed foods as much as possible.