where does one park when flying out of Oakland?

The there terminal is not at Oakland Airport proper but the Oakland Municipal Airport.

The only parking mentioned in the JetSuiteX site is the CurbStand valet for $32/day. You can also take a chance on the nearby lots as mentioned in the previous answer, or just use a taxi/rideshare service.

There are several parking lots directly across the street from the JetsuiteX terminal. They may say there is a limit on how long you can park there but that is not the case.