I have accidentally sent BCC from bittrex to my own BTC wallet on coinbase. Both wallets are mine - how can I get (find out) my private keys to swap them that I get my money from wrong chain? And how can I use these private keys? Transaction is seen here:
If it was your wallet, you'd have no issue, a BTC address can hold and spend BCC, but you sent it to coinbase's wallet in effect which you do not have the private keys for.
By Jan 2018, they have said they will support BCC. I would hope that would be when you would see it, but no guarantees as they operate off-chain, who knows how they work internally. So I would contact their support for clarification.