Holden has been kicked out of at least three schools, but it's not clear whether he was kicked out of the others. He has been kicked out of Pencey Prep at the beginning of the novel for flunking his classes, and his teacher Spencer says, "If I’m not mistaken, I believe you also had some difficulty at the Whooton School and at Elkton Hills."
However, Holden clarifies Spencer's remarks and says that he wasn't kicked out of Elkton Hills but instead quit the school. Holden found the headmaster at Elkton Hills, Mr. Haas, a phony, as he cozied up with stylish parents and wasn't as friendly with parents he considered gauche or not up to snuff. Holden tells Spencer that being at Elkton Hills depressed him so much that he had to quit the school. Therefore, Holden has attended at least three schools, but it's not clear if he was kicked out of the others or simply chose to leave them.