RotationTransition

final Tween<double> turnsTween = Tween<double>(
  begin: 1,
  end: 3,
);

AnimationController _controller;

bool _first = true;

initState() {
  _controller = AnimationController(
    vsync: this,
    duration: const Duration(seconds: 1),
  );
  super.initState();
}

@override
Widget build(BuildContext context) {
  return Column(
    mainAxisSize: MainAxisSize.min,
    children: <Widget>[
      RotationTransition(
        turns: turnsTween.animate(_controller),
        child: Container(
          child: Container(
            width: 200,
            height: 200,
            padding: EdgeInsets.all(20),
            child: FlutterLogo(),
          ),
        ),
      ),
      SizedBox(height: 20,),
      FlatButton(
        onPressed: () {
          if (_first) {
            _controller.forward();
          } else {
            _controller.reverse();
          }
          _first = !_first;
        },
        child: Text(
          "Click Me!",
        ),
      )
    ],
  );
}