Where does a rocket keep oxygen to burn?

Only liquid fuelled rockets (and then only some) rely on oxygen as the oxidizer. It is carried in liquid form in a tank (or tanks). It is them pumped and mixed with the fuel in the combustion chamber where the combustion reaction takes place. The combusion products then exit the rocket nozzle.

In solid fuel rockets, the oxidizer (whatever that may be) is usually mixed with the fuel.