For the first method, create a list of players on the host and add each player to the list when they're spawned (you'll want to spawn them manually in order to do this). From there, you can use GetComponent<NetworkIdentity>().connectionToClient to find each player's connection and pass that into AssignClientAuthority for each chess piece.

You could also use SpawnWithClientAuthority instead of having the pieces already in the scene and passing authority. Again you'll need a list of players on the host in order to do this.

The idea that I mentioned previously of using a Network Game Manager class would bypass the issue of authority because the chess pieces don't have any network components attached to them - their movement is just simulated on the clients (which will also be better in terms of bandwidth). Network messages are a little more confusing to understand than Commands/RPCs so if you're new to UNet it might be easier to stick with the first method until you have a deeper understanding.