One area of gameplay I have not explored deeply is how characters can escape with the combined use of their abilities and terrain. Are there guides that detail where on the map specific characters can use their abilities to escape (which walls are thin enough?) I often see Tryn escape from the dragon pit with his spin. Also, which walls are easily flashable, moderately hard to flash, and extremely hard to flash over? I would like it in one big guide.

one thing i hate about escaping, it always seems like i cant catch the other guy im "chasing" or my team is chasing, but everyone catches me. I need tier 5000 boots to get away.

There isn't such a guide as far as I know, but really it comes down to 2 things:

1: know how far your flash/jump is or how long you can stay stealthed.

2: Do what your enemy wouldn't expect. Run towards the river or their base when they can't see you, flash into their base (and hide in the blind spot behind the tree) Stand still in the bush and wait for them to enter it before running away.

The main reason for getting caught is being predictable or not knowing the limits of your flashes/stealths

Basically any champion with displacement ability can do it.
Once you know all of the characters and abilities this should not be a problem for you.

My suggestion take nidalee for a custom game try jumping different walls and stuff (remember to face it directly). You now know what walls nidalee and renekton can cross (maybe I missed a champion or two with similar displacement range). (or search a site like mobafire to see pictures)

Take ezreal for a custom game, try jumping different walls and things. Now you know what walls you can jump with flash, and what walls pretty much all other champions with displacement can jump. Pretty much all walls are jumpable with these types of champions.

There is really no easy/hard/extremely hard walls to jump over, you either can jump over it or you can't just get as close to the wall as possible and use your ability.

I suggest you use smart casting (shift+ ability, or rebind your keys), it saves half a second which can change affect if you live or die.

Also another things to note is that Jax and Lee Sin can jump to walls, if you have smart casting enabled it is possible to run to wall place ward and jump to it fast enough.

Use bushes to your advantage and don't act predictably. i.e. move towards their base not yours.