I've painted a lot of brass models, including brass etchings as well as brass investment castings. I've never found the need to etch them with vinegar or even apply a primer, but I've used enamel based paints for all of my brass painting projects, the paint of choice being Scalecoat II.
However, since Scalecoat II is out of business, I've been resorting to other enamels, such as Testors, and I've been having good luck with their enamel based paints.
The trick is to make sure your brass is completely de-greased, de-waxed and clean. I use my ultrasonic cleaner with a potent ammonia-based solution that's for de-investing lost wax castings. I also use Bestine (Heptane) rubber cement thinner and wax solvent to get rid of any stray waxes that might be adhering to the brass.
Also, when I airbrush, I make sure the paint is going on wet. If it's drying too quickly, I need to get closer or reduce the air pressure a bit. You don't want paint to go on really wet, but wet enough for it to retain a smooth surface and not creating orange-peel or a rough finish. The mineral spirits in the paint need to help the pigments bond to the metal, and if the paint is going on too dry, it's just the pigments that are sticking to the metal surface, and they will flake off.
I'm also trying Tru-color paints, and so far, the results are good and it seems to be as durable as old Scalecoat II. One caveat is that I thin it at least 25& with Tru-color thinner before shooting in my internal-mix Paasche VL airbrushes. My next brass project I'll be using Tru-color primer on it because on my last Aijin/Overland brass caboose paint job, I had some flaking...which I've never had before. Not sure just exactly why, but I'll be taking steps to make sure it doesn't happen again, which includes primer.
Also, when painting, I wear fresh Nitrile gloves to handle my brass models after they've been thoroughly cleaned and de-greased/de-waxed. The gloves are also a convenient surface to test my airbrushes output immediately before brushing my model, so my left Nitrile glove always has odd spray patterns on it when I finally peel them off!
Hope this might be of some assistance to you...
Cheerio!
Bob Gilmore