Levelling up skinning has become a lot easier in Legion, because level 100-110 mobs do not drop leather scraps like they used to do in previous expansions. They used to only drop scraps for players with too low skill level, and regular skins for players with sufficient skill, but now they drop the same no matter if the skinning skill level is 50 or 500.
In order to level skinning, simply skin mobs from the Broken Isles zones, and you gain one level per skin. Both Stormheim, Val'sharah, Azsuna and Highmountain has skinable creatures, but the best area to level skinning in is around the Hemet Nesingwary area in Highmountain. This place provides a lot of beast focused quests that a lot of players do, so you can use this area so skin the creatures they kill for the quest.