A number of people seem to have difficulty soldering zinc around their projects. This is because zinc transmits the heat quickly – more quickly than the tin/lead solder – requiring more heat to be put into the process. There is a solder that can make this process easier as it is designed for soldering zinc.
“Galvanite is a lead-free galvanizing solder formulation designed specifically for high quality repairs to galvanized steel surfaces. Simple, effective and easy to use, in both manufacturing and field applications. It metallurgically bonds to the steel, for a seamless protective barrier.”
It composition is 50% tin, 49% zinc and 1% copper. It becomes solid at 200C and liquid at 300C. This makes it a high temperature solder for stained glass purposes, but will give a firm attachment between the zinc and the solder or lead came it surrounds. The high temperature aspect means you need to keep the iron on the zinc rather than the more easily soldered metals or the glass.