EDIT: there is no fixed scale for jazz. It's just a big mish mash of notes done properly.

actually there are rules. . . and when you say a big mish mash of notes then you're wrong. . . that is what jazz musicians call atonality. . . go wiki it. . .

but you should start off with basic be-bop scales and jazz minor scales. . .

get a hang of it then move on to whole tone / half tone, super locrian, and all that other stuff. . .

atonality also requires you to have good sense of timing and polyrhythm. . .

on the random notes thing. . . if you actually ask a jazz musician what was it he plays. . . he can tell you exactly what he just did. . . so technically its not mish mash. . .

example i met a sax player who does the later miles (where he went electric) he studied in UK and he would play stuff that are just insane. . . when i asked him what he played he can show me the breakdown exactly and explain in detail why he choose those notes. . .

you can't just randomly hit notes and expect it to sound good. . . it ain't blues where the scales are always perfect and safe. . .

even when it comes to atonality there a strict rules and boundries to it. . .

it may sound wierd cause people are not used to the scale. . . hearing a foreign scale will sound alien to new ears. . .

and jazz musicians work around the chords too. . . there are unlimited ways to approach a chord so sometimes you have different keys in a single bar. . .