You are missing the https:// in your url.

Replace the code below with your url() method:

  String url() {
    if (Platform.isAndroid) {
      // add the [https]
      return "https://wa.me/$phone/?text=${Uri.parse(message)}"; // new line
    } else {
      // add the [https]
      return "https://api.whatsapp.com/send?phone=$phone=${Uri.parse(message)}"; // new line
    }
  }

I found a solution adding this code to android/app/src/main/AndroidManifest.xml

<queries>
<intent>
    <action android_name="android.intent.action.VIEW" />
    <data android_scheme="https" />
</intent>
<intent>
    <action android_name="android.intent.action.DIAL" />
    <data android_scheme="tel" />
</intent>
<intent>
    <action android_name="android.intent.action.SEND" />
    <data android_mimeType="*/*" />
</intent>

 String url() {
      if (Platform.isIOS) {
        return "whatsapp://wa.me/$phone/?text=${Uri.encodeFull(message)}";
      } else {
        return "whatsapp://send?phone=$phone&text=${Uri.encodeFull(message)}";
      }
    }

This worked me by adding this code to android/app/src/main/AndroidManifest.xml below </Application> Tag:

<queries>
        <!-- If your app opens https URLs -->
        <intent>
            <action android_name="android.intent.action.VIEW" />
            <data android_scheme="https" />
        </intent>
        <!-- If your app makes calls -->
        <intent>
            <action android_name="android.intent.action.DIAL" />
            <data android_scheme="tel" />
        </intent>
        <!-- If your sends SMS messages -->
        <intent>
            <action android_name="android.intent.action.SENDTO" />
            <data android_scheme="smsto" />
        </intent>
        <!-- If your app sends emails -->
        <intent>
            <action android_name="android.intent.action.SEND" />
            <data android_mimeType="*/*" />
        </intent>
    </queries>

Method i used to open Whatsapp:

void openWhatsapp(
      {required BuildContext context,
      required String text,
      required String number}) async {
    var whatsapp = number; //+92xx enter like this
    var whatsappURlAndroid =
        "whatsapp://send?phone=" + whatsapp + "&text=$text";
    var whatsappURLIos = "https://wa.me/$whatsapp?text=${Uri.tryParse(text)}";
    if (Platform.isIOS) {
      // for iOS phone only
      if (await canLaunchUrl(Uri.parse(whatsappURLIos))) {
        await launchUrl(Uri.parse(
          whatsappURLIos,
        ));
      } else {
        ScaffoldMessenger.of(context).showSnackBar(
            const SnackBar(content: Text("Whatsapp not installed")));
      }
    } else {
      // android , web
      if (await canLaunchUrl(Uri.parse(whatsappURlAndroid))) {
        await launchUrl(Uri.parse(whatsappURlAndroid));
      } else {
        ScaffoldMessenger.of(context).showSnackBar(
            const SnackBar(content: Text("Whatsapp not installed")));
      }
    }
  }

The plugin works fine, but you need to add the permissions in the android manifest for opening issues as of android 11: https://github.com/flutter/flutter/issues/90099

Two things that helped me:
Phone number should be pure number.
Country code should be the prefix with + sign.

Like +14564564562

I am using this dependency url_launcher: ^5.4.1 in my project to launch whatsapp through my flutter application but when i am pressing button to launch application it is not working but showing an error message on emulator that could not open the link.
given below is the code with function i am using to launch whatsapp.

import 'package:flutter/material.dart';
import 'package:url_launcher/url_launcher.dart';
import 'dart:io';


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

class Wapp extends StatelessWidget {
  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      title: 'Flutter Demo',
      theme: ThemeData(
          primarySwatch: Colors.orange,
      ),
      home: MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  MyHomePage({Key key, this.title}) : super(key: key);

final String title;

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

class _MyHomePageState extends State<MyHomePage> {
 void launchWhatsApp(
    {@required int phone,
    @required String message,
    }) async {
  String url() {
    if (Platform.isAndroid) {
      return "whatsapp://wa.me/$phone:03452121308:/?text=${Uri.parse(message)}";
    } else {
      return "whatsapp://send?   phone=$phone&text=${Uri.parse(message)}";
    }
  }

  if (await canLaunch(url())) {
    await launch(url());
  } else {
    throw 'Could not launch ${url()}';
  }
}


Widget build(BuildContext context){
  return Scaffold(
    appBar: AppBar(
      title: Text("Home"), 
    ),

  body: Center(
    child: RaisedButton(
      
      color: Colors.orange,
      textColor: Colors.black,
      padding: EdgeInsets.symmetric(vertical: 20.0, horizontal: 60.0),
      highlightColor: Colors.green,
      onPressed: () {
        launchWhatsApp(phone: 03452121308, message: 'Hello');
      },
      child: Text("Place Your Order",style: TextStyle(
          
          fontWeight: FontWeight.bold,
          fontSize: 15
          
        )
      )
    )
  )

  );
}

}