1) Get to know about Slash's early years... do some research and find out what kind of music influenced his development, and then listen to that yourself.
2) Learn your modes... this will take some time, but its an attainable goal. Part of learning about modes though should include recognizing tonal centers. For instance, if you play the Cmaj scale and the A minor scale, its the exact same notes. However, one has a tonal emphasis around C, and the other A. Get used to playing the same notes, but "hearing" the tonal center being Cmaj, or A minor. If you come up with a little riff using the notes of the C maj scale over a C major chord progression, that riff will sound like a major scale riff. You should be able to hear that. If you suddenly change the chord progression to Aminor, that riff will suddenly sound minor, even though the notes are the same. This really helps with what your after, because you can listen to riff that someone like Slash is using, slowly work it out for yourself, and then figure out the tonal center that is defining the scale. I know it sounds a bit confusing, but think back to the Cmaj/Amin example. If I just showed you a riff using those notes, you might say "oh, its Cmaj" or "oh, is Amin..." either is correct... its whether the riff feels like its resolving to C or A that will define the actual mode.
3) Check out sites like "Lick Library"... they have some really good "pay-per-lesson" deals on GNR songs like "Sweet Child 'O Mine"... learning some of Slashes stuff note for note will really help you get a grasp of what he's doing stylistically, especially if you've done your homework. That's not a bad song to learn either because Slash does that very identifiable key change in the later half of the song.
Good luck!