Rémi Rousselet, thank you very much. Your advice has helped. Below is the prototype of function that I need:
  OverlayEntry
    _modeless = null;
  void _showModeless(BuildContext context)
  {
     _modeless = new OverlayEntry(
        opaque: false,
        builder: (context) {
          return new Positioned(
            top: 100.0,
            left: 100.0,
            child:
            new Row(
              mainAxisAlignment: MainAxisAlignment.start,
              crossAxisAlignment: CrossAxisAlignment.center,
              children: <Widget>[
                new Icon(Icons.content_paste, color: Colors.blueGrey),
                  new Padding(
                    padding: const EdgeInsets.only(left: 16.0),
                    child: new Text('Modeless', overflow: TextOverflow.ellipsis,
                      style: new TextStyle(fontSize: 14.0, fontWeight: FontWeight.bold, color: Colors.lightBlue, decoration: TextDecoration.none
                      ),
                    ),
                  ),
              ],
            ),
          );
        });
    Overlay.of(context).insert(_modeless);
     _startWaiting();
  }
 static const TIMEOUT = const Duration(seconds: 8);
 static Timer _timer = null;
  void _startWaiting()
  {
    _timer = new Timer(TIMEOUT, _handleTimeout);
  }
  void _handleTimeout()
  {
    if (_modeless != null)
      _modeless.remove();
  }
PS. I added only another function that allows to remove the modeless after 8 sec. Once again many thanks.