Displaying notification badge on BottomNavigationBar's Icon

One more variation of counting badge (implemented with Stack of Icon and wrapped in Container Text, which stretched when counter increase):

BottomNavigationBarItem(
  icon: new Stack(
    children: <Widget>[
      new Icon(Icons.notifications),
      new Positioned(
        right: 0,
        child: new Container(
          padding: EdgeInsets.all(1),
          decoration: new BoxDecoration(
            color: Colors.red,
            borderRadius: BorderRadius.circular(6),
          ),
          constraints: BoxConstraints(
            minWidth: 12,
            minHeight: 12,
          ),
          child: new Text(
            '$_counter',
            style: new TextStyle(
              color: Colors.white,
              fontSize: 8,
            ),
            textAlign: TextAlign.center,
          ),
        ),
      )
    ],
  ),
  title: Text('Notifications'),
),

Yes. It can be done by stacking two icons using the Stack and Positioned widget.

      new BottomNavigationBarItem(
        title: new Text('Home'),
        icon: new Stack(
          children: <Widget>[
            new Icon(Icons.home),
            new Positioned(  // draw a red marble
              top: 0.0,
              right: 0.0,
              child: new Icon(Icons.brightness_1, size: 8.0, 
                color: Colors.redAccent),
            )
          ]
        ),
      )

You can also nest the Stacks. For instance, if you would like to add item_count on the shopping_cart icon, you can do this:

icon: new Stack(
              children: <Widget>[
                new Icon(Icons.shopping_cart),
                new Positioned(
                  top: 1.0,
                  right: 0.0,
                  child: new Stack(
                    children: <Widget>[
                      new Icon(Icons.brightness_1,
                          size: 18.0, color: Colors.green[800]),
                      new Positioned(
                        top: 1.0,
                        right: 4.0,
                        child: new Text(item_count,
                            style: new TextStyle(
                                color: Colors.white,
                                fontSize: 15.0,
                                fontWeight: FontWeight.w500)),
                      )
                    ],
                  ),
                )
              ],
            )