使用file_picker（https://pub.dev/packages/file_picker）包，它允许选择任何扩展名的文件。
样本代码：-

FilePickerResult? result = await FilePicker.platform.pickFiles(
  type: FileType.custom,
  allowedExtensions: ['jpg', 'pdf', 'doc'],
);

完整代码：-

import 'package:flutter/material.dart';

import 'package:file_picker/file_picker.dart';

void main() => runApp(const Example());

class Example extends StatefulWidget {
  const Example({super.key});

  @override
  State<Example> createState() => _ExampleState();
}

class _ExampleState extends State<Example> {
  openExplorer() async {
    FilePickerResult? result = await FilePicker.platform.pickFiles(
      type: FileType.custom,
      allowedExtensions: ['jpg', 'pdf', 'doc'],
    );
    if (result != null) {
      print("File selected");
    }
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
          body: GestureDetector(
              onTap: (() {
                openExplorer();
              }),
              child: const Center(child: Text("Open Gallery")))),
    );
  }
}

输出：-