Do I need to flush rewrite rules when creating new user if using custom author rewrite rules?

Yes, you should flush rewrite rules in this case, because you add rules for every author based on his nicename.

To be more precise, you should flush them after any author changes his nicename also.

And you do this using author_rewrite_rules hook, which is fired in wp_rewrite_rules() only when there are no rules in database. So without flushing them your filter won’t be fired and your new rules won’t be added.