When you say you have a single ticket: do you mean that you have actually one single ticket number covering your trip from HKG to SEA? Or did you (or an OTA) make two bookings?

I have never seen combined JX + CX tickets before. If it is indeed a single ticket (issued by CX or JX), that would be a strong indication that an interlining agreement is in place and thus through checking of bags would be possible.

CX CS will be able to give you a definitive answer.

Edit: Actually JX seems to sell fares involving travel on CX, explicitly allowing routing on CX flights, so I would assume that there is an interlining agreement in place, but best to check with JX or CX customer service.