你可以复制粘贴下面运行完整的代码
您需要使用https://pub.dev/packages/path_provider来获取临时目录
代码片段

RaisedButton.icon(
                onPressed: () async {
                  var tempDir = await getTemporaryDirectory();
                  String fullPath = tempDir.path + "/boo2.pdf'";
                  print('full path ${fullPath}');

                  download2(dio, imgUrl, fullPath);
                },
                icon: Icon(
                  Icons.file_download,
                  color: Colors.white,
                ),
                color: Colors.green,
                textColor: Colors.white,
                label: Text('Dowload Invoice'))

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工作演示
100d1x

的字符串
完整代码

import 'package:flutter/material.dart';
import 'package:dio/dio.dart';
import 'package:path_provider/path_provider.dart';
import 'dart:io';

final imgUrl =
    "https://www.w3.org/WAI/ER/tests/xhtml/testfiles/resources/pdf/dummy.pdf";
var dio = Dio();

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      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> {
  int _counter = 0;

  void _incrementCounter() {
    setState(() {
      _counter++;
    });
  }

  Future download2(Dio dio, String url, String savePath) async {
    try {
      Response response = await dio.get(
        url,
        onReceiveProgress: showDownloadProgress,
        //Received data with List<int>
        options: Options(
            responseType: ResponseType.bytes,
            followRedirects: false,
            validateStatus: (status) {
              return status < 500;
            }),
      );
      print(response.headers);
      File file = File(savePath);
      var raf = file.openSync(mode: FileMode.write);
      // response.data is List<int> type
      raf.writeFromSync(response.data);
      await raf.close();
    } catch (e) {
      print(e);
    }
  }

  void showDownloadProgress(received, total) {
    if (total != -1) {
      print((received / total * 100).toStringAsFixed(0) + "%");
    }
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: Text(widget.title),
      ),
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            RaisedButton.icon(
                onPressed: () async {
                  var tempDir = await getTemporaryDirectory();
                  String fullPath = tempDir.path + "/boo2.pdf'";
                  print('full path ${fullPath}');

                  download2(dio, imgUrl, fullPath);
                },
                icon: Icon(
                  Icons.file_download,
                  color: Colors.white,
                ),
                color: Colors.green,
                textColor: Colors.white,
                label: Text('Dowload Invoice')),
            Text(
              'You have pushed the button this many times:',
            ),
            Text(
              '$_counter',
              style: Theme.of(context).textTheme.display1,
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: _incrementCounter,
        tooltip: 'Increment',
        child: Icon(Icons.add),
      ),
    );
  }
}

型

您必须添加权限。
对于Android：在AndroidManifest.xml

<manifest...
    <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
    <uses-permission android:name="android.permission.INTERNET"/>

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pubspec.yaml
ext_storage：^1.0.3
your.dart

@override
  void initState() {
    getPermission();
    super.initState();
  }

  //get storage permission
  void getPermission() async {
    await PermissionHandler().requestPermissions([PermissionGroup.storage]);
  }

型

我无法将PDF保存到此路径

final directory = (await getTemporaryDirectory()).path;

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最后能够保存文件到/storage/emulated/0/Download/使用下面的方法来检查是否download或downloads路径存在和优先级：

Future<String> _getPath() async {
    String directory;
    if (Platform.isIOS) {
      directory = (await getDownloadsDirectory())?.path ??
          (await getTemporaryDirectory()).path;
    } else {
      directory = '/storage/emulated/0/Download/';
      var dirDownloadExists = true;
      dirDownloadExists = await Directory(directory).exists();
      if (!dirDownloadExists) {
        directory = '/storage/emulated/0/Downloads/';
        dirDownloadExists = await Directory(directory).exists();
        if (!dirDownloadExists) {
          directory = (await getTemporaryDirectory()).path;
        }
      }
    }
    return directory;
}

型
你的Future<void> download2()方法没有问题。
我也没有使用这个权限：

<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />

型
因为从android 10开始，存储权限标记为deprecated permission_handler，并使用MANAGE_EXTERNAL_handler代替。

<uses-permission android:name="android.permission.MANAGE_EXTERNAL_STORAGE"/>

型
注意事项：
Flutter稳定：3.16.3
dio：^5.4.0
permission_handler：^11.1.0