K.,
Kids frequently mimic what they see Mom and Dad doing. I can drink a gallon of milk in about a day and a half. My husband will only drink white milk with Lasagna or Spaghetti. My son is 5 and will drink both white and chocolate. My daughter is 18 months and will occasionally drink white, but is more like her dad and prefers chocolate.
I just kept offering and kept offering until she drank some. It can take her a day or more to drink 10oz of white, but about 5 minutes to drink the same in chocolate. Once I realized that we keep both types of milk in the house. She's only really been drinking white milk for a few months, and even then it's still hit and miss. Talked to her doctor about it and was told that as long as she's drinking it doesn't really matter what flavor it is. There are added antioxidants in chocolate milk that white milk doesn't have.
The other importance about milk is not the dairy aspect of it, but the fats. Like you said they can get dairy from cheese and yogurt, but they need the fats in, preferably, whole milk to help with their brain development. They need these until they are at least 2 years old.
Don't know if this helped or not, but good luck.
Melissa