在我打开一个issue之后，livekit团队添加了新功能。
解决方法如下：

EventsListener<RoomEvent> _listener
Room room
...

Future<bool?> showConfirmDialog() async{
  //here we show an alert dialog requesting permission
}

void _setUpListeners() => _listener
   
    ..on<AudioPlaybackStatusChanged>((event) async {
      if (!room.canPlaybackAudio) {
        print('Audio playback failed ..........');
        bool? yesno = await showConfirmDialog();
        if (yesno == true) {
          await room.startAudio();
        }
      }
    });