Make no mistake, giving regular tea to a dog would not be a great idea. Canine heart rates are high as it is. The last thing you'd want to do is hop up a dog on caffeine, which isn't great for dogs (neither is milk or sugar).
One tea company, California Tea House, has manifested this thought in an actual product: Machu's Blend, Tea for Dogs. They claim:
After consulting with numerous veterinarians, and compiling research on herbal treatments for canines, we put our tea blending skills to work for our canine companion. Machu's Blend tea for dogs is a once-a-day herbal tea comprised of Chamomile, Ginger Root, Fennel Seed, Skullcap and Calendula that not only promotes healthy skin and coat for your dog, but also lowers stress and aids digestion of dry dog food, easing the stomach and reducing gas. In addition, Machu's Blend is great for the prevention of bloat and treating dogs that suffer from seizures as well as motion sickness caused by car rides.
Beyond that, there's an additional whole line of herbal teas for dogs called Woof and Brew — five different blends allegedly perfect for pooches.
I still wouldn't recommend it, but there it is.