Zinc metal parts are generally galvanised to prevent rust and oxidation and help them hold up over long periods of time. Unfortunately, this makes them slick, causing resistance to paint adhesion. You can't just slap a coat of primer and paint on zinc or you will end up with chipping and peeling over time. If you want to paint zinc metal parts, you need to know the proper preparation techniques or you will end up with a finish that won't hold up.
Remove the oil from the galvanisation process from the zinc parts by scrubbing them with a water-based degreaser and a coarse brush. Rinse the parts thoroughly and allow them to dry before continuing.
Lay the parts on a heavy-duty fabric dust sheet.
Prime the surface to encourage adhesion by spraying the parts with zinc cold galvanising compound. Apply in intermittent sprays rather than one constant stream to avoid drips and runs.
Allow the zinc parts to dry for two full hours and then apply zinc spray paint in the same manner as you did the galvanising compound.
Never attempt to prime zinc with ordinary bonding primer or you will end up with chipping.