It should be okay. The things-to-check with primer are i) What colour is the top-coat and ii) What type of paint will you put on top of it?
If you have a dark paint, chances are your original primer was light grey. The zinc will be darker grey but on a chip, you won't see any difference.
Your primer and paint are probably both cellulose, in which case they'll be compatible with each other. Pro' paints are often acrylic and don't like sitting on top of cellulose primer etc.
The zinc will be good to protect the metal, since it will offer some galvanic protection. Build up the layers slowly (take your time, even over several days) so that the primer is almost the same level as the surrounding paint.. and then top off with the colour.
You want the colour to be "raised" ever so slightly so you can eventually polish it down to the same level as the rest of the paint.
No bullets for Chaingun..