I can't seem to find him...any tips?

I found this on another website:

"After defeating the Elite Four, Suicune will be released into the fields of Kanto. But there is no easy way to catch one of the Legendary Dogs.

What I always do to capture the Legendary Dog, is waiting until he appears and then I make sure he can't flee with a move like Spider Web or Mean Look. Make sure the Pokémon knowing this move has a significant higher speed than Suicune, so he can do his move first.

Now he can't flee anymore. Paralyse him and lower his HP as much as you can. An ideal move is False Swipe, which leaves your opponent with at least 1 HP (so it can't knock out a Pokémon).

So now he has only 1 HP and is paralysed. Throw some Ultra Balls (or another one like a Timer ball if your battle lasted long) to it and it will be captured eventually."

I mean like what happens when it's on a route?

Hmm.. I don't know. You should check out the threads linked below this one. It seems this has been discussed before.

Nothing! It keeps on appearing and appearing until you defeat him or catch him.