I know INFJ's are characterized as good writers, which brings Jess to mind, but I think I'd put him in the ISFP mode. Although I think people often fit more than one type, so he has some INFJ characteristics. But, here's something on the ISFP: (quotes in quotes, my comments afterwards)
ISFPs may be quite charming and ingratiating on first acquaintance, flowing with compliments which may (or may not) be deserved. On other occasions, the same individual may be aloof and detached. Some ISFP males are fiercely competitive, especially in sport or table games, and may have great difficulty losing. This competitive nature, also seen in other SP types, sometimes fosters 'lucky,' 'gut' feelings and a willingness to take risks.
Okay, the first sentence isn't Jess. But, aloof and detached, I think he definitely was when he first came to Stars Hollow. And, although I think he's grown out of that some, I don't think he'll ever want to be the center of attention in a crowd. Fiercely competitive? Well, I think Jess got as much pleasure out of beating Dean as he did of winning Rory's affections. Don't know about the gut feeling, though.
Organized education is difficult for the majority of ISFPs, and many drop out before finishing secondary education. Their interest can be held better through experiential learning, at which many excel. ISFPs will practice playing an instrument or honing a favored skill for hours on end, not so much as practice as for the joy of the experience.
Jess didn't finish high school. I don't know his learning style, since that wasn't a factor in his storyline. He doesn't play an instrument, but I could see him honing his reading and writing skills just because he liked to do it.
But, then, you come up to the brick wall that ISFP (Introverted Sensing Feeling Perceiving) aren't thought to be good writers. On the other hand, the writing thing sort of got tacked on to him in season 6, instead of building up naturally. I mean, it makes sense, I buy it, but I don't recall any sign that it's where the character was going back when he was a regular. Readers don't all end or want to end up as writers.
Here's a snippet of INFJ that fits Jess, and doesn't fit:
INFJs have a knack for fluency in language and facility in communication. In addition, nonverbal sensitivity enables the INFJ to know and be known by others intimately.
Fluency in language, check. Know others intimately? Maybe. Be known? I don't know about that. I