how we can use two rows in appbar flutter Like first row with title and the second with search input field

you can customize the size of app bar by using toolbarHeight: 120.0 // set value then use flexibleSpace to add column or rows it will look something like this

import 'package:flutter/material.dart';

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

class App extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        appBar: AppBar(
          toolbarHeight: 120.10, //set your height
          flexibleSpace: SafeArea(
            child: Container(
              color: Colors.blue, // set your color
              child: Column(
                children: [
                  Row(
                    children: [Text("Logo")],
                  ),
                  Text("data"), // set an icon or image
                  IconButton(
                      icon: Icon(Icons.search),
                      onPressed: () {}) // set your search bar setting
                ],
              ),
            ),
          ),
        ),
      ),
    );
  }
}

Just simply create your AppBar as intended, in your screenshot, you don't actually need a second Row. A TextFormField will be enough (you will actually need to customise the InputDecoration as well):

    return AppBar(
      title: Column(children: [
        Row(children: [
          Icon(Icons.menu),
          Text('First row'),
          const Spacer(),
          Icon(Icons.person),
        ]),
        TextFormField(),
      ]),
    );

You can use the bottom property from the AppBar widget.

AppBar(
    title: YourFirstRowWidget(),
    centerTitle: true,
    bottom: PreferredSize(
        child: YourSearchBarWidget(),
        preferredSize: null),
  )

But you may want to create your own AppBar widget for a perfect result.