I usually hear it as "Been there, done that, got the t-shirt" all as one.
When you go on vacation, it's common to come back with something as a keepsake. A t-shirt is a common thing to bring back. You go to St. Thomas, you come home with a St. Thomas t-shirt.
The phrase you're asking about is usually not used literally - it is used to mean "That's not new to me; that's not exciting; that's something I've done before."