I used to do a lot of home repair work for people. When I would install galvanized gutters and down spouts, I used a galvanized primer that I bought at Sherwin-Williams before i painted the gutters. The primer was a bluish color and it felt almost like a plastic coating when it dried.
Seemed to work pretty well - at least I never got any callbacks for peeling paint. You might check with Sherwin-Williams.
Tom in TN