When I look at a song like Crazy Train or something like that, he does these fills in each chorus, and especially the second and last fill, how does that fit in with theory? Is that Chromatic?
he's most likely using the Natural Minor scale to play runs where you're talking about.

Like that. And he does it to the 14, then 15 then 16 exc. What kind of theory is that?
there really isn't any "theory" in this. people use chromaticity to either move to a new key area or to "create tension," and i believe that's what rhoades was going for before he returned to the main riff of the chorus
Quote by hawk_kst
That lick is just an F minor lick...

He moves up the whole next of that, by a semi tone, I think it's called. I've seen a lot of people do that, where they make a cool lick and just go with it.
yeah, just take a lick and move it up the neck one fret at a time.

other examples:

Rock & Roll (Zep), 1:57 - 1:59 of the solo, climbs up the neck

Highway Start (Deep Purple), the end of the solo, goes down the neck on the first string:

--15-14-0-0----14-13-0-0----13-12-0-0----- etc
When using Chromatic scales in this way, do I start a lick on the Key signature, but then just move it up and up until I end on a key signature? How does that work exactly?
I'd say generally you're going to end up on a note that is in key - because what these sort of ascending or decending licks are doing to is moving from one place to another and they typically end on a held note that would have to fit the song or else it would sound crappy. The chromatics can work because they're usually played pretty quickly and are just notes that are between where you're starting and ending.
Yeah I don't really see licks out of key that are being played solo. Does it start and end on the Key? Or does it just start anywhere and end on key?