I have listened to a lot of Slash when I was a young guitarist. And his technique isn't the same as Vai's or Satch's. Practicing scales and things like that to a metronome will make you play cleanly and fast (like VAI or Satch), while Perry, Slash and others have some kind of 'dirty' bluesy feel in everything they play.
So try to play blues lines, and then increase your speed by playing faster. Listen to Stevie Ray Vaughan too, great fast bluesy player there.