They might love fanfiction because it offers new perspectives on their own lives. In fanfictions, their characters can be developed in ways that the original show might not have explored fully. For instance, they could be portrayed as more complex individuals with deeper backstories.
I'm not sure specifically as there could be many different versions of such a fanfiction. But generally, it might be about Ash coming to the rescue of Jessie and James in some sort of dangerous or difficult situation they are in within the Pokémon universe.
One common theme is unrequited love finally being realized. For a long time in the Pokémon show, their relationship was more of a comical partnership, but in fanfiction, the kiss can be a moment of that underlying love coming to the surface.
Well, there is definitely some 'jessie and james kiss fanfiction' around. If you're into more romantic - themed ones, you might find some where the kiss is a turning point in their relationship. Others could be more comical, like it happens by accident during one of their zany schemes in the Pokémon series.
In fanfiction, the jealousy of Jessie towards James might be a creative way to explore their characters more deeply. It could be that the author wants to show Jessie's insecurities. For example, if the fanfiction has James being praised for his skills or looks, Jessie, who is often portrayed as competitive, might feel jealous because she wants that kind of recognition too. Also, it could be related to her possessive nature over James as a partner in their Team Rocket adventures.
Meowth would be a great addition. He could provide comic relief while also being part of Team Rocket's adventures related to the lemon theme. Also, Pikachu could be involved. Maybe Jessie and James try to use lemons to attract Pikachu in a new and strange way. And Butterfree, as it could be related to the pollination of lemon trees in the fanfiction.
One possible storyline could be that Jessie and James, after years of being Team Rocket members, decide to leave that life behind. They realize their love for each other while on a Pokemon adventure. In the fanfiction, they might start a new life in a peaceful Pokemon - filled region, perhaps opening a Pokemon - themed cafe. Their Pokemon would also be part of their new life, with Meowth helping out in the cafe.