The InAppBrowser class represents a native WebView displayed on top of the Flutter App, so it’s not integrated into the Flutter widget tree.

You can use the InAppBrowser.webViewController property, that is an instance of the InAppWebViewController class, to control the InAppBrowser instance.

To be able to listen to the WebView events, you need to create a class that extends the InAppBrowser class in order to override the method callbacks.

Example:

import 'dart:io';

import 'package:flutter/material.dart';
import 'package:flutter_inappwebview/flutter_inappwebview.dart';

class MyInAppBrowser extends InAppBrowser {
  @override
  Future onBrowserCreated() async {
    print("Browser Created!");
  }

  @override
  Future onLoadStart(url) async {
    print("Started $url");
  }

  @override
  Future onLoadStop(url) async {
    print("Stopped $url");
  }

  @override
  void onLoadError(url, code, message) {
    print("Can't load $url.. Error: $message");
  }

  @override
  void onProgressChanged(progress) {
    print("Progress: $progress");
  }

  @override
  void onExit() {
    print("Browser closed!");
  }
}

Future main() async {
  WidgetsFlutterBinding.ensureInitialized();

  if (Platform.isAndroid) {
    await AndroidInAppWebViewController.setWebContentsDebuggingEnabled(true);
  }

  runApp(
    MaterialApp(
      home: MyApp(),
    ),
  );
}

class MyApp extends StatefulWidget {
  final MyInAppBrowser browser = new MyInAppBrowser();

  @override
  _MyAppState createState() => new _MyAppState();
}

class _MyAppState extends State<MyApp> {
  var options = InAppBrowserClassOptions(
      crossPlatform: InAppBrowserOptions(hideUrlBar: false),
      inAppWebViewGroupOptions: InAppWebViewGroupOptions(
          crossPlatform: InAppWebViewOptions(javaScriptEnabled: true)));

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('InAppBrowser Example'),
      ),
      body: Center(
        child: ElevatedButton(
            onPressed: () {
              widget.browser.openUrlRequest(
                  urlRequest: URLRequest(url: Uri.parse("https://flutter.dev")),
                  options: options);
            },
            child: Text("Open InAppBrowser")),
      ),
    );
  }
}

This is the result:

Android basic usage.
iOS basic usage.