Example of how to compose a TabBar + TabBarView + NestedScrollView + CustomScrollView + SliverAppBar.

example_tab_bar_view.dart

import 'dart:math' as math;

import 'package:flutter/material.dart';

void main() => runApp(Main());

class Main extends StatefulWidget {
  @override
  State<StatefulWidget> createState() => _MainState();
}

class _MainState extends State<Main> with SingleTickerProviderStateMixin {
  final _tabs = <String>['Colors', 'Search', 'Settings'];
  TabController _tabController;

  @override
  void initState() {
    super.initState();
    _tabController = TabController(length: _tabs.length, vsync: this);
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        body: NestedScrollView(
          headerSliverBuilder: (context, innerBoxIsScrolled) {
            return [
              SliverOverlapAbsorber(
                handle:
                    NestedScrollView.sliverOverlapAbsorberHandleFor(context),
                sliver: SliverAppBar(
                  pinned: true,
                  automaticallyImplyLeading: false,
                  primary: false,
                  collapsedHeight: 160.0,
                  expandedHeight: 260.0,
                  forceElevated: innerBoxIsScrolled,
                  flexibleSpace: Container(
                    alignment: Alignment.bottomCenter,
                    padding: EdgeInsets.only(
                        top: MediaQuery.of(context).viewPadding.top),
                    child: LayoutBuilder(
                      builder: (context, BoxConstraints constraints) {
                        final height = constraints.biggest.height.truncate();
                        return Column(
                          mainAxisAlignment: MainAxisAlignment.center,
                          children: [
                            Expanded(
                              child: Center(
                                child: Text('Height: ${height}'),
                              ),
                            ),
                            Container(
                              color: Colors.red,
                              height: 60.0,
                              child: Material(
                                color: Colors.transparent,
                                child: TabBar(
                                  controller: _tabController,
                                  labelStyle: TextStyle(
                                    fontWeight: FontWeight.w700,
                                  ),
                                  indicatorWeight: 4.0,
                                  tabs: _tabs.map((tabName) {
                                    return Tab(
                                      child: Text(
                                        tabName,
                                        style: TextStyle(
                                          fontWeight: FontWeight.w800,
                                        ),
                                      ),
                                    );
                                  }).toList(),
                                ),
                              ),
                            ),
                          ],
                        );
                      },
                    ),
                  ),
                ),
              ),
            ];
          },
          body: TabBarView(
            controller: _tabController,
            children: _tabs.map((tabName) {
              if (tabName == _tabs.first) {
                return MyColors();
              } else if (tabName == _tabs[1]) {
                return Container(color: Colors.green);
              } else {
                return Container(color: Colors.orange);
              }
            }).toList(),
          ),
        ),
      ),
    );
  }
}

class MyColors extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Builder(
      builder: (context) {
        return CustomScrollView(
          slivers: [
            SliverOverlapInjector(
              handle: NestedScrollView.sliverOverlapAbsorberHandleFor(
                context,
              ),
            ),
            SliverFixedExtentList(
              itemExtent: 50.0,
              delegate: SliverChildBuilderDelegate(
                (context, index) {
                  final Color color = _randomColor();
                  return Container(
                    color: color,
                    height: 50.0,
                    child: Text('${index}. Color: $color'),
                  );
                },
                childCount: 20,
              ),
            ),
          ],
        );
      },
    );
  }

  Color _randomColor() {
    final colors = <Color>[
      Color(0xFFb78443),
      Color(0xffFC5457),
      Color(0xFF124559),
      Color(0xFFbe56ca),
      Color(0xFF3e5641),
      Color(0xFF4f0fb3),
      Color(0xffFC5457),
      Color(0xFF222f5b),
      Color(0xFFacb873),
      Color(0xFF2979FF),
      Color(0xffFC5457),
      Color(0xFF680cee),
      Color(0xFF6464dd),
      Color(0xFF1d4ffe),
      Color(0xFFacb873),
      Color(0xffFC5457),
      Color(0xFF6464dd),
      Color(0xFFbe56ca),
      Color(0xffFC5457),
      Color(0xFF6699ee),
      Color(0xFF2979FF),
      Color(0xffF2C573),
      Color(0xffE37338),
      Color(0xffFC5457),
      Color(0xfffe1d4f),
      Color(0xFF2979FF),
    ];
    return colors[math.Random().nextInt(colors.length)];
  }
}