a "dirty jess" is a sexual term for oral sex. Most commonly known as "extreme 69" but more intense, where at the end, both of the participants float away in a hamster wheel.
A dirty Jessie is a act where a person pisses in someone's mouth whilst that someone has previously had multiple laxatives thus creating a hot running mess of shit that a lucky recipient starts to eat.
This is also commonly know as the "in one, out the other trick"
A dirty Jess is licking out your dog while your cat watches then you proceed to shit in your own mouth swallow it and shit in your dogs mouth. It's a repeated cycle.