Is there any milk left in the refrigerator? No, I/we/your brother finished it. (standard) No, it's finished. (also pretty common) "It's finished" wouldn't be a good answer to "do you have milk?" because the answer to that could be "no" even if you never had any milk at all. But you certainly could hear this for any kind of question that is basically asking whether the milk has been consumed.

No, it is finished or over usually refers to an action or an activity or a performance. For example: I finished my homework. My homework is finished. (activity) The movie/concert/play/show/song is over. (performance) I finished practicing the piano. (action) My piano lesson is over. (activity) In your example, you could say: Q: Do you have any milk? A: No, it's gone. No, I'm out. No, the carton is empty.

No, "it´s finished" doesn´t work in English, though you would probably be understood. Better replies would be "No, it´s all gone", "No, there´s none left", "No, I/we don´t have any (left)". Hope this helps. It´s a good question because in Spanish it would work, so it may work in other latin based languages as well, I don´t know, but no, it doesn´t work that way in English.