I haven't done the Liver Flush yet, but I asked the same question.
The answers I got were No, you do not need the walnut tincture.
YOur flush should be just as effective.
If you notice, in this website, the ingredients don't call for it, but are listed in the directions. I plan on doing one on Saturday but I will not be using the Walnut Ticture.
Good luck with your results and please share them with us. I would love to har about it.