```dart
import 'dart:io';
import 'package:path_provider/path_provider.dart';

Future<void> downloadProtected(String cognitoIdentityId) async {
  // Create a file to store downloaded contents
  final documentsDir = await getApplicationDocumentsDirectory();
  final filepath = documentsDir.path + '/example.txt';
  final file = File(filepath);

  // Set access level and Cognito Identity ID.
  // Note: `targetIdentityId` is only needed when downloading
  // protected files of a user other than the one currently
  // logged in.
  final downloadOptions = S3DownloadFileOptions(
    accessLevel: StorageAccessLevel.protected,

    // e.g. us-west-2:2f41a152-14d1-45ff-9715-53e20751c7ee
    targetIdentityId: cognitoIdentityId,
  );

  // Download protected file and read contents
  try {
    await Amplify.Storage.downloadFile(
      key: 'ExampleKey',
      local: file,
      options: downloadOptions,
    );
    final contents = file.readAsStringSync();
    safePrint('Got protected file with contents: $contents');
  } on StorageException catch (e) {
    safePrint('Error downloading protected file: $e');
  }
}
```