School me - Do modern flat tappet cams/lifters need high-zinc oil?

I drive Vixen more than that. I've been trying to drive her more lately. I change it when it gets dirty pretty much. That usually equates to once yearly.
We may put 1000 miles in a week in a van, and not start a Duster in 3 months. Just how it is.... I got rid of a couple, but still have too many classics.. LOL