Airline code JC is used by Japan Air Commuter(non oneworld partner). So, you can't earn Avios/TP.

JAL Express no longer exists. JAL Express airline code JC is REUSED by non oneworld partner Japan Air Commuter.

Bad/Curious/Good from a certain point of view,
JAL(Japan Air Commuter) accepts Oneworld elite status for non-oneworld JC flights(operated by Japan Air Commuter).
You have lounge access, priority boarding, priority check-in etc.

Also, JAL online reservation system accepts your BAEC number for JC(Japan Air Commuter) flight even though the flight is non-mileage accrual/non partner.

In my experience, I registered my BAEC number to JAC2322(JC2322) from TJH to ITM.
Avios calculator shows 70 Avios for Y class (Yes. it's very short flight).
However, this flight was operated by JAC, so I couldn't earn Avios.
I had to contact BA and JAL several times to re-credited this flight to my JAL account.