For those of you who have read the book, you know that the TV show is extremely different (as in they added and subtracted characters). So we can do both the book and the tv show separately.
TV SHOW: (We don't really know enough about them yet, but this is just based after the first episode. I'm sure opinions will change as the season progresses.)
Elena: INFP. (My friends tell me that I want everyone to be an INFP though. One of them suggested that she might be an E, but became more introverted after her parents died. But I don't know ... she seems to live an intense internal life.)
Jeremy: Don't know yet.
Mrs. Flowers: INFJ.
Freaky Twins: ENTJ.