Example code for issue described at: https://github.com/flutter/flutter/issues/27887 and https://stackoverflow.com/q/54647229/1027507

nested_scroll_demo.dart

import 'package:flutter/material.dart';

void main() async {
  runApp(new TestApp());
}


class TestApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return new MaterialApp(
      theme: new ThemeData(primarySwatch: Colors.yellow),
      home: new TestAppHomePage(),
    );
  }
}

class TestAppHomePage extends StatefulWidget {

  @override
  State createState() => new TestAppHomePageState();
  //FPDetailScreen({Key key, @required this.period}) : super(key: key);
}

class TestAppHomePageState extends State<TestAppHomePage>
    with SingleTickerProviderStateMixin {

  @override
  Widget build(BuildContext context) {

    return new Scaffold(
      //bottomNavigationBar: bottomNavBar,
      body: DefaultTabController(
        length: 2,
        child: NestedScrollView(
          headerSliverBuilder: (BuildContext context, bool innerBoxIsScrolled) {
            return <Widget>[
              SliverAppBar(
                expandedHeight: 120.0,
                floating: false,
                forceElevated: innerBoxIsScrolled,
                backgroundColor: Colors.green,
                pinned: true,
                flexibleSpace: FlexibleSpaceBar(
                  collapseMode: CollapseMode.pin,
                  centerTitle: true,
                  title: Text(
                    "Foo Bar Baz",
                    style: TextStyle(color: Colors.white),
                    textAlign: TextAlign.left,
                    overflow: TextOverflow.ellipsis,
                    softWrap: true,
                    maxLines: 1,
                  ),
                  background: Container(
                    alignment: Alignment.topCenter,
                    child: Column(
                      mainAxisAlignment: MainAxisAlignment.spaceEvenly,
                      children: <Widget>[
                        Row(
                          children: <Widget>[
                            Text(
                              '10.00 TL',
                              style: TextStyle(
                                  color: Colors.white,
                                  fontSize: 20.0,
                                  fontWeight: FontWeight.bold),
                            ),

                          ],
                          mainAxisAlignment: MainAxisAlignment.center,
                        ),
                        Container(
                          width: 0,
                          height: 0,
                        )
                      ],
                    ),
                  ),
                  //background: ,
                ),
              ),
              SliverPersistentHeader(
                pinned: true,
                delegate: _SliverAppBarDelegate(
                  TabBar(
                    tabs: [
                      Tab(
                        child: Text(
                          "Tab1",
                          style: TextStyle(
                              color: Colors.black,
                              fontWeight: FontWeight.bold),
                        ),
                      ),
                      Tab(
                        child: Text(
                          "Tab2",
                          style: TextStyle(
                              color: Colors.black,
                              fontWeight: FontWeight.bold),
                        ),
                      ),
                    ],
                  ),
                ),
              ),
            ];
          },

          body:TabBarView(
              //controller: _tabController,
              children: [
                CardList(),
                CardList(),
          ]),
        ),
      ),

    );

  }
}

class _SliverAppBarDelegate extends SliverPersistentHeaderDelegate {
  _SliverAppBarDelegate(this._tabBar);

  final TabBar _tabBar;

  @override
  double get minExtent => _tabBar.preferredSize.height;
  @override
  double get maxExtent => _tabBar.preferredSize.height;

  @override
  Widget build(
      BuildContext context, double shrinkOffset, bool overlapsContent) {
    return new Container(
      color: Colors.white,
      child: _tabBar,
    );
  }

  @override
  bool shouldRebuild(_SliverAppBarDelegate oldDelegate) {
    return false;
  }
}




class CardList extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: ListView.builder(
          scrollDirection: Axis.vertical,
          shrinkWrap: true,
          itemCount: 20,
          //itemExtent: 1.0,
          itemBuilder: (context, index){
            return new ListTile(
              title: new Text("Item $index"),
            );
          }),
    );

  }
}