Scaling content on drag down in Flutter

I want ot achieve this behavior in Flutter.

Do you know if there is a built-in widget in Flutter that provides that fuctionality out of the box?

try this CustomScrollView:

LayoutBuilder(
  builder: (context, constraints) {
    return CustomScrollView(
      slivers: <Widget>[
        SliverPersistentHeader(
          pinned: true,
          delegate: Delegate(),
        ),
        SliverToBoxAdapter(
          child: Container(
            decoration: BoxDecoration(
              borderRadius:  BorderRadius.all(Radius.circular(30)),
              border:  Border.all(
                width: 2.0,
                color:  Colors.deepPurple,
              ),
            ),
            height: constraints.biggest.height,
            child: Center(
              child: Text('Drag me down (or up) in order to see (or hide) the red icon on the top',
                textAlign: TextAlign.center,
                textScaleFactor: 5.0,
              ),
            ),
          ),
        ),
      ],
    );
  }
),

the "delegate" class is as follows:

class Delegate extends SliverPersistentHeaderDelegate {
  @override
  Widget build(BuildContext context, double shrinkOffset, bool overlapsContent) {
    // print(shrinkOffset);
    return Opacity(
      opacity: 1 - shrinkOffset / maxExtent,
      child: FittedBox(child: Icon(Icons.alarm, color: Colors.red,), fit: BoxFit.contain),
    );
  }
  @override double get maxExtent => 300;
  @override double get minExtent => 100;
  @override bool shouldRebuild(SliverPersistentHeaderDelegate oldDelegate) => true;
}

now try to drag the text up and down

EDIT: and this is a little modification to be similar like your example:

LayoutBuilder(
  builder: (context, constraints) {
    return CustomScrollView(
      slivers: <Widget>[
        SliverPersistentHeader(
          pinned: true,
          delegate: Delegate(),
        ),
        SliverToBoxAdapter(
          child: Container(
            padding: EdgeInsets.only(top: 75),
            height: constraints.biggest.height,
            child: Text('Drag me down (or up) in order to make the red icon bigger (or smaller)',
              textAlign: TextAlign.center,
              textScaleFactor: 5.0,
            ),
          ),
        ),
      ],
    );
  }
),

and the modified delegate class:

class Delegate extends SliverPersistentHeaderDelegate {
  @override
  Widget build(BuildContext context, double shrinkOffset, bool overlapsContent) {
    // print(shrinkOffset);
    return OverflowBox(
      maxHeight: 400,
      alignment: Alignment.topCenter,
      child: Container(
        height: 400 - shrinkOffset,
        child:  FittedBox(child: Icon(Icons.alarm, color: Colors.red,), fit: BoxFit.contain),
      ), 
    );
  }
  @override double get maxExtent => 300;
  @override double get minExtent => 1;
  @override bool shouldRebuild(SliverPersistentHeaderDelegate oldDelegate) => true;
}