At least for AA, I’ve always been able to book award from with QR Avios *from* QR served cities (ie JFK-MEX) via the app, but never from non-QR served cities (ie MEX-JFK). But have always been able to book those flights by checking availability on BA and then calling QRPC to make the booking (bit of a headache since it can turn into an hour+ ordeal with a couple of callbacks involved)