The Cool Roof laboratory has validated a primer on galvanized steel (galvanized steel = steel coated with zinc).

We will therefore consider that the primer proposed for galvanized steel is also suitable for zinc.
Furthermore, if the zinc sheet is new, it is (theoretically) recommended to remove the etching before applying the primer: either mechanically (sanding or sandblasting) or possibly chemically (using a de-etching agent).
Please contact us for more information.