If I was betting on it, I would have said within 20 minutes and on an empty stomach. You should get nauseous, at least, but the contents of your stomach might be enough to hold it down.
I haven't eaten anything in 4 hours. I had 12 pills in one swallow each of which apparently has two and a half times the RDI of zinc for males. I haven't experienced any nausea. If I head eaten a dozen oysters on the other hand I am almost certain I'd have vomited. But that says a lot more about my aversion to oysters than their zinc content.
More generally I can confirm that taking vitamins on an empty stomach most certainly does produce more acute side effects. For example I tried a pharmacological dose of niacin (1g) on an empty stomach and apart from the intense pain and flushing over my entire body I was extremely nauseous and nearly passed out. The same dose with a meal only gives me a mild, almost pleasant tingling sensation - albeit one that lasted longer.
Now... no more zinc for me for a couple of weeks.
Pictures or it didn't happen.