Edit your ListTile -  trailing: as follow:

trailing: new Column(
  verticalDirection: VerticalDirection.down,
  children: <Widget>[
    Flexible(
        child: new IconButton(
            icon: Icon(Icons.arrow_drop_up), onPressed: () {})),
    Flexible(child: new IconButton(icon: Icon(Icons.arrow_drop_down), onPressed: () {}))
  ],
),