I did a web search and I was partially wrong. The acid is not to etch the surface, creating a rough pattern to help the paint stick. It appears there is a deposit on galvanizing when it leaves the factory that should be removed before painting. (Some sites call it waxy, some call it chalky, some just say there is a deposit, some don't mention it.) The three recommended ways are to let it age (I saw four and six month recommendations, depends on the site) lightly sandpaper it, or use a mild acid wash. Some sites did not mention removing it at all.
Now, back to opinion and observations.
As with painting your house, the right surface preparation will give you a better paint job. You don't have to chip and scrape and power wash, but some of us do. I don't go to that much trouble with everything I paint, either. Depends on what I am painting and why. I'm not painting my buried galvanized wire around the coop. I figure at my age the galvanizing will probably last longer than me anyway.
The galvanized material that is going in the ground (such as buried fencing or aprons around the coop or run to deter predators) is exactly where I would recommend painting it. I asked the professionals offshore why they were painting the galvanized material. They told me it was to extend the life. On one platform, they showed me galvanized grating that had been accidently oversprayed when the supports and grating was replaced. (The grating support member was painted, the the grating was galvanized. They were replaced at the same time.) The pure galvanized material was rusted away. The grating that had been accidently sprayed (without a special surface prep, by the way, but it may have been aged) looked like new. The oil companies are not going to spend big money to paint something to make it pretty. They are trying to avoid spending much bigger money replacing it. And even a bad paint job made a big difference.
I don't know which primer is the best to use with which topcoat. There are many products out there and I'm sure most of them will work fine, just read the label directions. The folks at the paint store will probably be able to help, at least as far as their products go. And I don't know how long to leave the vinegar on. The guys offshore were washing it off after a few minutes. It did not smell like vinegar but I would guess it was pretty mild. You would not want the acid to eat off the galvanizing, just that coating.
LynneP makes a good point. The vinegar and the rinse water will contain some product of the chemical reaction. I would not let them drink from puddled rinse water and would probably do this prep work away from the birds if possible. I also would not let the birds have access to the painted fencing until it was dry just like I would not spray my fruit trees when he chickens are downwind. Think about what you are doing and take appropriate precautions.
My final $0.02 worth. From what I have seen and what the professionals showed me, even a bad paint job will greatly extend the life of galvanized material.