Of course I would know the answer to this question because I need to buy milk for my store because I am after all in the ice cream business. It recently has been a challenge for myself as well.
Because of all of the ridiculous increases in Manhattan along with runaway inflation many local markets have decided not to carry milk and certain types of dairy. I have read that NYC's regulations have gotten quite strict and for many markets it's just not worth it for them to carry regular milk.
It's really no surprise to me when all the big supermarkets are suffering in Manhattan besides Wholefoods. I read a lot of business magazines so I can understand why we are seeing this trend in Chinatown as well.
So to answer the question: Where is it possible to buy milk in Chinatown?
(1) Duane Reade on the Bowery (Btw Bayard and Canal)
(2) Dynasty Supermarket (Btw Hester and Grand)