Dynamic characters undergo some significant change during the course of a novel. Static characters remain the same. I don’t think Jordan Baker changes much, so I would call her a static character. Jordan is detached, unsentimental and materialistic. She uses people and therefore fits in well with the upper class world of superficial socialites. When Jordan and Nick meet for the last time, it is clear that she has not changed. Nick has decided not to play games anymore and to move on. In the last chapter, she does say that being with an honest straightforward person was a new experience for her, but it did not affect her enough to make a permanent change.
In the story of "The Great Gatsby," Jordan represents a fairly STATIC character. Of course, to say that we should probably be certain we understand what a "static character" is.
When something it "static" that means it doesn't change much (or that it will give you a shock when you touch it : ) This is contrasted with a "dynamic" character, which means one that will change a lot during the course of a story. A dynamic character grows and learns, when a static one doesn't.
The proof, really, is in the fact that Jordan is pretty much the same type of girl she was at the end of the story as she was at the beginning of the story. She starts out a little aloof with aspirations of thinking she is better than most people, and toward the end she sort of remains that way. It is probably one of the reasons why Nick never takes a "serious" interest in her...she is a little bit boring.
In fact, most of the characters in Gatsby are a bit static. None of them really changes much during the course of the story. Daisy has a bit of a melt-down for a while, but by the end she is back where she started. Gatsby dynamic nature occurs largely outside of the story, such as his growing up period that we don't really get to see first hand. And Nick, though he does develop certain sensibilities during the story, isn't radically different after that crazy summer.