```dart
Future<void> downloadPrivateFile(String cognitoIdentityId) async {
  ...
  final downloadOptions = S3DownloadFileOptions(
    // Add the private access level
    accessLevel: StorageAccessLevel.private
    ...
  );

  try {
    await Amplify.Storage.downloadFile(
      ...
      // Be sure to use the correct options
      options: downloadOptions,
    );
    ...
  }...
}
```