The short answer: No.
The long answer: There are two main reasons why cats should not drink chocolate milk. The first reason is because cats cannot have chocolate. Chocolate is a treat prepared using roasted and ground cacao seeds. Served in liquid, paste, or block form, chocolates contain the compound theobromine, the stimulant caffeine, and sugar that can all cause life-threatening complications to your cat. As little as 0.2 ounces of baking chocolate, 0.5 ounces of semi-sweet chocolate or dark chocolate, and 1.14 ounces of milk chocolate can poison an 8-pound cat.
Secondly, chocolate milk generally uses cow milk. Most adult cats cannot drink cow milk because they do not have the digestive enzyme necessary to break down the lactose found in cow milk. As such, letting your cat drink chocolate-flavoured milk is a no-no.
What to do if your cat accidentally drinks chocolate milk: Observe your cat for diarrhea, bloating, intestinal cramps, upset stomach, and vomiting in the next 24 hours. Depending on how much chocolate is in the milk drink, she may also exhibit hyperactivity, restlessness, increased thirst, tremors, increased reflex responses, muscle rigidity, rapid breathing, and seizures. A trip to the veterinarian or animal emergency clinic is needed.
In summary: Chocolate milk should not be given to your cat, even as an occasional treat. The ingredients found in both cow’s milk and chocolate can cause digestive upset and toxic poisoning. If you are interested in giving milk to your cat, do your research to discover which kinds of milk are safe for her. Make sure they do not contain chocolate or other lethal flavourings. More importantly, get your veterinarian’s approval before making her try it.