I have a DONE3 Issued by QR, how should I change the flights to the right codeshare?

So what is the tool I use to find the BA flight numbers and how do i convince QR to do it?

Actual metal flights QR/QR/BA/BA/AA/AA/AA/AA/JAL/CX/CX/CX/CX/BA/BA - wasnt smart enough to ask to use codesharing

CAI-DOH-IKA-MEX-MIA-JFK-LAX-HNL-NRT-HKG-MLE-HKG-BOM-LHR-DXB

Finally decided with everyones' help to go for BA EC and get OWE