You can just use a container inside the dialog with custom BoxDecoration:

Dialog(
  child: Container(
    decoration: BoxDecoration(
      color: Colors.white,
      boxShadow: const [
        BoxShadow(
          color: Colors.red,
          blurRadius: 10)])));

See demo here: https://dartpad.dev/?id=d3f1fb7d3e50e1543f6899c57c7effb8