Kakashi can too use wind style he uses resengan which is wind style this is during his teaching Naruto with the wood user. So I guess I have my answer he can use all styles.

Kakashi can use wind style, too. He uses the Rasengan, which is a wind style jutsu. This is during his teaching Naruto with the wood user Yamato. So, I guess I have my answer: he can use all styles.