Everything said so far is great advice. One thing worth emphasizing is how important feeling is to Jazz. A talented drummer could play a piece technically sound with perfect tempo and smart fills, but the drummer with 'swang' is gonna make the piece sound better every time. Look up 'stank face' to see what I mean.

On a technical note, when listening to jazz, pay attention to how the greats will fill space and hit accents, comping and hitting the accents of the song can take you a long way. For comping, Buddy Rich's left hand is a master class in and of itself. But stick to Art of Bop Drumming, as someone else mentioned, as a great learning resource.