I googled this because I find it interesting, but black tea does not contain tannic acid. It contains tannins, but of a completely different type (antioxydants which actually seem to be healthy). I couldn't find anything definitive on whether adding milk is a good idea or not. Maybe it helps for some people.
That's interesting. I wasn't 100% when I posted, it was from memory. On a little checking, it seems we're both right -- tannic acid is a subset of tannins. In any case, milk seems to help, whatever the mechanism.