AnimatedOpacity

double opacityLevel = 1.0;

void _changeOpacity() {
  setState(() => opacityLevel = opacityLevel == 0 ? 1.0 : 0.0);
}

@override
Widget build(BuildContext context) {
  return Column(
    mainAxisAlignment: MainAxisAlignment.center,
    children: [
      Container(
        height: 120.0,
        width: 120.0,
        color: Colors.blue[50],
        child: AnimatedOpacity(
          opacity: opacityLevel,
          duration: Duration(seconds: 3),
          child: FlutterLogo(
            size: 60,
          ),
        ),
      ),
      RaisedButton(
        child: Text('Fade Logo'),
        onPressed: _changeOpacity,
      ),
    ],
  );
}