Does a zinc metal coating react with coffee in a coffee grinder?
If you plate the pieces with zinc or silver, the main source of zinc/silver in the ground coffee will be from abrasion between the parts and the coffee beans and not from chemical attack.

A few milligrams of zinc or silver (or iron for that matter) won't to do any harm to your health, specially if diluted in many coffee cups along several months or years.

In fact, Zinc was used therapeutically in dosages upwards of hundreds of milligrams per day for months, or more, with no permanent health issues.

Silver, on the other hand, has much lower acceptable exposure limits and while not particularly toxic, I'd not put it in parts of the device that are guaranteed to put metallic silver into the ground beans.