I don't take a zinc supplement, so I'm not really going to answer your question. My multi has zinc as does a calcium supplement that I sometimes take. While I don't consciously seek out foods high in zinc, several things I routinely eat seem to cover me.
Zinc is important and one of those that if you don't eat well as a veg*n you might be low in, so it's a good question.
Here's a couple of good articles for readers of this thread, that show which foods to eat and how to help absorption. How much to take in a supplement isn't really suggested, but one says 1/2 of the RDA as well as eating well should cover you.