From what I understand, there isn't sufficient data to say that dairy increases mucus, <b>but</b> I can say it effects me. If I drink a lot of milk or yogurt consistently for several days, I will start wheezing.
I think it is different for everyone though. I know it effects me, but maybe not the next person. You might want to test it out by stopping the chocolate milk for a week or two and see if your child breathes more easily.