TL; DR

现在已实现为插件

const url = "https://flutter.io";
if (await canLaunch(url))
  launch(url);
else 
  // can't launch url, there is some error

完整示例：

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

void main() {
  runApp(new Scaffold(
    body: new Center(
      child: new RaisedButton(
        onPressed: _launchURL,
        child: new Text('Show Flutter homepage'),
      ),
    ),
  ));
}

_launchURL() async {
  const url = 'https://flutter.io';
  if (await canLaunch(url)) {
    await launch(url);
  } else {
    throw 'Could not launch $url';
  }
}

在pubspec.yaml中

dependencies:
  url_launcher: ^5.4.2

特殊的角色：

如果该url值包含网址中现在允许的空格或其他值，请使用

Uri.encodeFull(urlString)或Uri.encodeComponent(urlString)，而是传递结果值。