In Lords of the Fallen, the Flayed Skin is an important quest item that will help you unlock the Dark Crusader class. I will explain where you can get the flayed skin first and then move towards how to use it. I highly recommend completing the quest it initiates before you fight and defeat the Light Reaper. If you progress further than that, then you will not get this quest.
Where to find flayed skin in Lords of the Fallen
Begin from Abandoned Redcop’s first vestige point. You reach this point after the tutorial crypt.

From the vestige point, run down the hill toward the arena where you had your first tutorial boss battle. Run through that arena in Lords of the Fallen and go right. Continue forward till you’ve reached a cliff edge, and you’ll notice the glow right next to you, indicating that there’s an item.

This item happens to be the Flayed Skin, which will begin your side quest to unlock the Dark Crusader secret class in the game.
How to use Flayed Skin
The Flayed Skin in Lords of the Fallen begins a secondary quest, and as an item, it evolves into an essential item called Umbral-Tinged Flayed Skin.
In order to get the Umbral-Tinged Flayed skin, you need to progress through the story a little and unlock a number of Stigmas related to Isaac the Paladin. After unlocking all the Stigmas, you’ll end up in a boss fight against “Paladin’s Burden.”
Defeating the boss would give you the Umbral-Tinged Flayed Skin. Now, you can use it to open the locked door at the location where you obtained the Flayed Skin. Behind this door, you’ll find a full set of Paladin Armor, which is basically the complete beginning armor set for the Dark Crusader.