zinc can oxidize... it creates a white powdery residue on the surface, but if you store it properly, it shouldnt be an issue.
as for arleigh's assertion, zinc doesnt sublimate until over 1670 degrees F... additionally it isnt going to fling out the barrel as the pressure inside of the cartridge is only going to make the plating adhere more permanently to the inside of the case. burning powder can exceed those temps, but not for long enough to transfer that heat into the case and chamber... even if it did get flung out the barrel, its much denser then air and wouldnt be an issue anyway.
nothing wrong with zinc plated cases... i store and have shot quite a bit of silverbear 5.45, have for years, no issues. just store in original packing or repack into ammo cans... just dont have it sitting in a puddle...