There is no known, or even concieveable, association between cheek implants and milk. This is a myth or wife's tale that I have never even heard of before.
In my more than 30 years of practice, I have never restricted this type of food to any of my patients after cheek, jowl, or chin implant surgery and I see no adverse effect from milk or any food as long as the wound is water-sealed closed.
I have performed many cheek implant procedures over the years and have never heard of any correlation between cheek implants and milk! Don't worry!