You can't, really. You can close your account, and you can email their support and ask them to delete all the information they hold on you, but you have no guarantee that they won't just say they've deleted it but actually continue to store it. Given how generally shady Coinbase's behaviour is, I think it is more than likely that they will continue to hold your information.
Down with Coinbase. LOL. alrighty then. its settled AND i think we can find a new place to bash now?