Where do the BCC go if an exchange doesn’t “support” it? So, it’s my understanding that any and all bitcoins will be duplicated on the BCC chain. So for all the exchanges that don’t support BCC, will they just pocket the coins? Especially since many of them have the user’s private keys?

Sorry if this shows a lack of understanding of the fork and blockchain, please enlighten me if I am confused.
As one popular Bitcoin advocate puts it, "your keys -- your bitcoin, not your keys -- not your bitcoin". Yes, the exchange can pocket your BCC, as well as it technically can pocket your BTC.

Even if an exchange declares BCC support, beware of accounting issues.