You don't need to fly on the airline which program you're doing the redemption on, that's the point of alliance partner redemptions.

USA is also a pretty broad destination designation, particularly when looking at nonstop options. Check for redemption options between your departure & arrivals points and if nothing appealing stands out do segment searches of origin to popular US entry point and then for entry to final destination as some searches get flummoxed.

UA search for Star Alliance, DL & KE for KE redemptions on Skyteam and BA followed by AA for OneWorld redemption options as BA is good at showing CX & DL options which AA is not great at but is better at showing AA availability over BA.