Create screen in the Flutter with TabBar in only one of the item of the bottom navigation bar.

bottom_navigation_with_tab_bar_screen.dart

import 'package:flutter/material.dart';

class TabBarWithBottomNavigationScreen extends StatefulWidget {

  @override
  _TabBarWithBottomNavigationScreenState createState() => _TabBarWithBottomNavigationScreenState();
}

class _TabBarWithBottomNavigationScreenState extends State<TabBarWithBottomNavigationScreen>  with SingleTickerProviderStateMixin {

  int _currentIndex = 1;
  bool _isShowTab = false;
  TabController _tabController;

  final List<String> _titles = [
    "Page 1",
    "Page 2",
    "Page 3"
  ];

  final List<Widget> _pages = [
    Container(color: Colors.orange),
    Container(color: Colors.yellow),
    Container()
  ];

  @override
  void initState() {
    super.initState();
    _tabController = TabController(length: 2, vsync: this);
  }

  @override
  Widget build(BuildContext context) {

    return Scaffold(
      body: DefaultTabController(
        length: 2,
        child: Scaffold(
          appBar: _isShowTab ? AppBar(
            title: Text(_titles[_currentIndex], style: TextStyle(color: Colors.red), textAlign: TextAlign.start,),
            iconTheme: IconThemeData(color: Colors.red),
            backgroundColor: Colors.white,
            bottom: TabBar(
              controller: _tabController,
              labelColor: Colors.red,
              tabs: <Widget>[
                Tab(text: "Page 3-1", icon: Icon(Icons.fastfood),),
                Tab(text: "Page 3-2", icon: Icon(Icons.phone_android),)
              ],
            ),
          ) : AppBar(
            title: Text(_titles[_currentIndex], style: TextStyle(color: Colors.red), textAlign: TextAlign.start,),
            iconTheme: IconThemeData(color: Colors.red),
            backgroundColor: Colors.white,
          ),
          body: _isShowTab ? getTabBarPages() : _pages[_currentIndex],
          bottomNavigationBar: BottomNavigationBar(
              onTap: onTabTapped,
              currentIndex: _currentIndex,
              backgroundColor: Colors.white,
              items: [
                BottomNavigationBarItem(
                  icon: Icon(Icons.business, color: Colors.grey,),
                  activeIcon: Icon(Icons.business, color: Colors.red,),
                  title: Text("Page 1"),
                ),
                BottomNavigationBarItem(
                    icon: Icon(Icons.card_giftcard, color: Colors.grey,),
                    activeIcon: Icon(Icons.card_giftcard, color: Colors.red,),
                    title: Text("Page 2")
                ),
                BottomNavigationBarItem(
                  icon: Icon(Icons.list, color: Colors.grey,),
                  activeIcon: Icon(Icons.list, color: Colors.red,),
                  title: Text("Page 3"),
                ),
              ]
          ),
        ),
      ),
    );
  }

  onTabTapped(int index) {
    setState(() {
      _currentIndex = index;
      if(index == 2)
        _isShowTab = true;
      else
        _isShowTab = false;
    });
  }

  Widget getTabBarPages() {
    return TabBarView(
      controller: _tabController,
      children: <Widget>[
        Container(color: Colors.green,),
        Container(color: Colors.blue)
      ],
    );
  }

}