Why am I getting no sound from my Amazon WorkSpace?
Amazon WorkSpaces client uses a Teradici Virtual Audio Driver which is initialized with the system Sound settings when the connection is first opened. Whatever Sound device was selected in System Preferences when the connection was established will continue to be the sound device for as long as the session was open.

In my case, I had to disconnect the WorkSpaces client, change the system Sound settings to use my bluetooth headset, then reconnect to WorkSpaces to get my sound working on the bluetooth headset.