AppBar wave shaped by quadratic bezier. DartPad: https://dartpad.dev/44fd77de9c38ab20c886ef04d55f5bc8

curved_bar.dart

// Credits to Matt Sullivan (@mjohnsullivan) for this status:
//   https://twitter.com/mjohnsullivan/status/1200142882864324609

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: AppBar(
          backgroundColor: Colors.purple,
          shape: Wave(
            heightOffset: 50,
            curvity: 80,
          ),
          title: Text('Curved AppBar'),
        ),
        body: Center(
          child: Text('Hello, World!',
              style: Theme.of(context).textTheme.headline3),
        ),
      ),
    );
  }
}

class Wave extends ContinuousRectangleBorder {
  const Wave({this.heightOffset = 20, this.curvity = 50});

  /// An offset in pixels to the standard AppBar height
  final double heightOffset;
  /// Curvity persent. 0% means straight line.
  final double curvity;

  @override
  Path getOuterPath(Rect rect, {TextDirection textDirection}) {
    double height = rect.size.height;
    double width = rect.size.width;
    return Path()
      ..lineTo(0, height + heightOffset)
      ..quadraticBezierTo(
        width / 4,
        height * (1 + curvity / 100) + heightOffset,
        width / 2,
        height + heightOffset,
      )
      ..quadraticBezierTo(
        width * 3 / 4,
        height * (1 - curvity / 100) + heightOffset,
        width,
        height + heightOffset,
      )
      ..lineTo(width, 0);
  }
}