Send an email notification once the MySQL stored proc executed

There is no direct support of such feature in MySQL RDS. Amazon RDS events supports only these categories https://docs.aws.amazon.com/AmazonRDS/latest/UserGuide/USER_Events.Messages.html

There are multiple programatic way you can achieve such notification e.g. Write status of stored proc in another table and let another client app keep polling for success/failure status and send email notification.