Hi, All bare metal should have a conditioner applied prior to primer, if not the paint will flake off. I've only painted galvanized once, it's been a long time. Very Very VERY stinky process to prep galvanized for primer! Have a good fitting resperator with the proper cartridge. This explains it better than I can
personally I advise against this, galvanized metal is most difficult to deal with and usually peels off
If you must, use a primer specifically designed for zinc coated metals (galvanized) & wash the item with thinner then with a strong oil cutting soap to remove the trace oils from the thinners
use polyurethane or 2 part epoxy paints, Alkyd/oil paints that are applied to galvanized metal will adhere initially, but will quickly peel. The zinc of the galvanizing will chemically react with the alkyd binder of the paint, creating a “soapy” film on the galvanized metal and causing the coating to peel.
this is much like concrete, if you paint it once you are committed to up keep, re-paint
although you may not be happy , hope this helps