The precise block is known to you but not me. If you said, I live in "the large block of flats", then I would say, "There are many large blocks of flats - which one do you mean?"
If you said, "I live in a block of flats", then you are telling me either that I don't need to know which one, or you are going to tell me later which one you mean. "a" is used to introduce the existence of a new (countable) thing to the reader or listener.