I'm no chemist but my first thought when a reader asked about adding vinegar to acrylic paint to turn it into fabric paint was that it didn't strike me as a good mixture, that you'd be better off simply using water-thinned acrylic.
For a definitive answer, I asked an expert, Sarah Sands, Technical Services Supervisor at Golden Artist Colors, who said:
Waterbased artists’ acrylics need to be in an alkaline environment to be stable and are very sensitive to changes in pH. In fact, if the overall pH drifts too much towards neutral you can often get a cottage-cheesy texture as the low pH will cause the binder to coagulate. As vinegar is an acid, it is the absolute opposite of where the acrylic system likes to be and adding even a small amount will likely cause it to react negatively and we would not recommend it. Although it is a good lesson in acrylic polymer chemistry!1
So, there you have it, vinegar and acrylic together is not a good idea.
The question did leave me wondering why someone would want to add vinegar, what the origin of the idea was. Was it somehow from that widespread but dubious tip about stopping the action of bleach on fabric with vinegar (see why not to mix bleach and vinegar)? Doing some digging it seems the most likely is it comes from the use of vinegar to help fix fabric dyes. But dyes and paint work differently: to vastly oversimplify it, dyes penetrate the fibers whereas paint sits on top. Placing a vinegar-soaked cloth over the acrylic paint before ironing won't help acrylic paint stick; it's the binder in the paint that does that, helped by the heat. Thin acrylic paint with fabruc-painting medium, such as Golden's GAC900, so it doesn't dry stiff like 'straight' acrylic paint does, then follow the heat-setting instructions (typically with an iron) if it requires. Or if stiffness doesn't matter, thin the paint with a little water and leave it dry a few days before washing it.
Reference: Email correspondence, August 2013.