You will have to store this data in the users device.
The shared_preferences package is very helpful for this.

For storing the data:

SharedPreferences perf = await SharedPreferences.getInstance();
perf.setBool(label, value);

For reading the data:

SharedPreferences perf = await SharedPreferences.getInstance();
bool isUserSignedIn = perf.getBool(label);

Here label is a String which is a unique identifer

For more information on the shared_preferences package use this link
https://pub.dev/packages/shared_preferences/example

Create a file called ROOTPAGE.dart and add the code to check if there is an existing user logen in. If a user id is found then go to home page else go to login,

 import 'package:name/pages/homepage.dart';
import 'package:name/pages/login_page.dart';
import 'package:flutter/material.dart';
import 'package:name/services/authentication.dart';

enum AuthStatus {
  NOT_DETERMINED,
  NOT_LOGGED_IN,
  LOGGED_IN,
}

class RootPage extends StatefulWidget {
  RootPage({this.auth});

  final BaseAuth auth;

  @override
  State<StatefulWidget> createState() => new _RootPageState();
}

class _RootPageState extends State<RootPage> {
  AuthStatus authStatus = AuthStatus.NOT_DETERMINED;
  String _userId = "";

  @override
  void initState() {
    super.initState();
    widget.auth.getCurrentUser().then((user) {
      setState(() {
        if (user != null) {
          _userId = user?.uid;
         
        }
        authStatus =
            user?.uid == null ? AuthStatus.NOT_LOGGED_IN : AuthStatus.LOGGED_IN;
      });
    });
  }

  void loginCallback() {
    widget.auth.getCurrentUser().then((user) {
      setState(() {
        _userId = user.uid.toString();
         authStatus = AuthStatus.LOGGED_IN;
        Navigator.of(context).pushReplacementNamed('/');
              });  });
  }

  void logoutCallback() {
    setState(() {
      authStatus = AuthStatus.NOT_LOGGED_IN;
      _userId = "";
    });
  }


  Widget buildWaitingScreen() {
    return Scaffold(
      body: Container(
        height: MediaQuery.of(context).size.height,
        width: MediaQuery.of(context).size.width,
       ......
      ),
    );
  }

  @override
  Widget build(BuildContext context) {
    switch (authStatus) {
      case AuthStatus.NOT_DETERMINED:
        return buildWaitingScreen();
        break;
      case AuthStatus.NOT_LOGGED_IN:
        return new LoginSignUpPage(
          auth: widget.auth,
          loginCallback: loginCallback,
          title: "name",
        );
        break;
      case AuthStatus.LOGGED_IN:
        if (_userId.length > 0 && _userId != null) {
          return new HomePage(
            userId: _userId,
            auth: widget.auth,
            logoutCallback: logoutCallback,
          );
        } else
          return buildWaitingScreen();
        break;
      default:
        return buildWaitingScreen();
    }
  }
}

pass this class to your main.dart

 home: new RootPage(auth: new Auth())

I have an auth class which has the login functions. adapt this code to help you solve your problem. Here is the getcurrent user func

Future<FirebaseUser> getCurrentUser() async {
FirebaseUser user = await _firebaseAuth.currentUser();
return user;

}

I have created a file for custom button as a widget function. But I need to use it in many places. But I need to route the page where I need at that time. How to achieve this? Please help!