I solve the gap closing problem with bilgewater cutlass, ghost and her W. I find getting other boots then mercs againt CC heavy teams or sorcery boots for the damage not that effective. Boots of mobility gives a large movement boost but only when you're not being attacked, which is not reliable. Boots of swiftness only gives 20 movement speed, I'd rather have the extra damage from sorcery boots. But if you want to take boots of swiftness, then I suggest you take exhaust because you won't need the movement speed buff from ghost but rather the slow from exhaust.
You are right on the CC teammates though, if you're team doesn't have enough CC, I suggest you take another champion.

I know how spell vamp works but why would a hextech hurt? Way more then 50% of her damage is magic damage, so why would it hurt?

I think I'm going to make a video or write a guide about how to play her, I'm getting the idea that the message I want to bring is not getting received.

Nice guide, you might wanna try other boots to solve the gap closure problems. Otherwise, a CC heavy team solves this issue. For all non-believers: Try it with a CCer in everylane, like morg mid, sona as support etc. Than you'll be fine. Had good experience with this build, thanks

I explained it in the guide, Shyvana's magic damage is about 50% magic damage on a standard build, with this proc build it's alot more because all of the procs deal magic damage.
The reason why I don't get alot of health is because I dont initiate with her, I kinda play her like a carry. And because I don't initiate I don't need the health, I need the damage.
I'll put something about teamfights in the guide.

I tested out this build and this build is ineffective, she lacks survivability. Getting Hextech Gunblade hurts her Ultimate, as spell vamp reduces AoE damage by 1/3 because of health gained.

"Q: How does spell vamp work?

A: Spell vamp works almost the exact same as lifesteal with one exception: An ability which naturally hits multiple targets (like Tormented Soil or Incinerate) is automatically 1/3 as powerful for the purposes of health gained"
-Quoted from: Frequently Asked Questions or Mechanics

Couple of things: While the damage, AS, and lifesteal is impressive, you lack health with this build. Shyvana is currently one of the most focused characters. Unless you hang back and do nothing, you'll need to get up in the opponents faces. I'm also confused with your quints and marks. AS is good, but why MPen? (Does it affect Q?) Same thing with the boots. I won't vote until I test this, but it seems really fragile.