I don't think that should be a problem, as long as the nicotine patch by itself does not have any ill effects on you. If you use it for 1-2 days with no problems then you can flush with that, too.
I haven't done that myself, by I confess to smoking quite a few cigarretes while doing the Liver Flush itself in the evening and next morning. I didn't have any problems.
Of course, you don't really want to smoke while LFing, but my point is that you most likely can Liver-Flush with the patch.