This Legion Skinning leveling Guide will show you the fastest and easiest way how to level your Legion Skinning from 1 to 100.
Leveling your Skinning will be easy, but you will have to run around and skin hundreds of mobs. Skinning is the best combined with Leatherworking.
Learning Legion Skinning
You can learn Legion Skinning by simply skinning mobs at the Broken Isle until you get 
Stonehide Leather Sample or Stormscale Sample. It's not 100% drop rate, but you should get it after a couple of mobs.
The reward for these quests is 
[Legion Skinner]. You only need to get one of these quests, you don't need both.
Don't forget to enchant your gloves with 
[Enchant Gloves - Legion Skinning]! This enchant brings skinning time down from 1.5 seconds to 0.5 seconds.
Leveling 1 - 100
Keep in mind! In Legion, several people can tag the same mob and still get loot. So, if someone tagged your mob but he didn't loot the corpse, you can't skin the mob.
I will only list a few zones here, if you want to find more skinning places, visit my Stonehide Leather farming guide, or the Stormscale farming guide.
Please note that even if a mob is red/orange to you, this doesn't guarantee that you'll get a skill up. It's more likely, but not to be expected every time.
Azsuna
These are level 45 mobs, so lower levels can't farm here.
Young Bloodgazers and Bloodgazer Nest-Keepers have really fast respawn rate, and the Young Bloodgazers have really low HP.
There are a couple of elite mobs patrolling around this area, you should avoid them, I think it's not worth to kill them.
When the Bloodgazer Swarm! world quest is active, there will be a lot of players there killing these mobs. So you will see dead animals everywhere, but most people don't loot the mobs, so sometimes it's actually worse to level here when the world quest is active.
Stormheim
You can find a lot of Saberfang Worg at the marked area.
Highmountain
This one is also the great place to farm Big Gamy Ribs. Sated Hillstrider will constantly keep spawning around the marked area.
I hope you liked this Legion Skinning leveling guide, congratulations to 100!