ffprobe/ffplay/ffmpeg command for checking audio/video sync
This tool is impossible. Almost.

To check sync of audio/video, you need something what appeared in both streams, what can be used as sync points. In old days used Clapperboard during film shooting. In television there was hidden timecode at border of frame, in zone of overscan which not displayed on TV

If you writing professional software, include timecodes to both streams. If not, just stream your video and audio in a single container, it enough.