Hi, We have heard yes and no on this issue. I have two girls w/CF. The oldest, Anna, doesn't drink milk because she says it makes her mouth slimmy and feels like she has more mucus. She will however eat ice cream and milk shakes, but not on a regular basis. She used to drink milk and didn't start complaining about his problem until she was in her teens. On the other hand, my younger daughter, Rachel, loves milk and drinks two or three tall glasses daily. Never has had a complaint that it makes her mouth slimmy or feels more mucusy.
I say, if he loves milk, especially chocolate milk, then let him have as much as he wants. He is getting good calories, and if you can find chocolate milk made with whole milk (impossible I'm sure) or he makes his own all the better. Plus he's getting Vit. D and Calcium which he needs even more so with CF.