Here, here! A present, child, an heirloom full of life! It was made of black serpent skins sewn together down two thirds of their length with silver thread. The snakes' tails, coiled together in a knot beneath her chin, twitched.
– Jame's narration, Dark of the Moon, "Chapter 13: Converging Paths"
The Cloak is made of the skins of snakes sewn together along their lengths, with the tails at the top and the heads at the bottom. The snakes appear to be alive and the Cloak as a whole is able to crawl away under its own power and will. Jame has briefly had possession of the Cloak, but it does not appear to have an affinity for her and slithers away when it gets the chance. It seems to be still in the Master's House in Perimal Darkling.
Like the other two objects of power, the Serpent-skin Cloak has an affinity for one of the Three-faced God's aspects. The cloak's orientation is with Argentiel, That-Which-Preserves. Accordingly, the Cloak's little-explored powers include healing. In Dark of the Moon, the Serpent-skin Cloak is able to combine with Kindrie to use the psychic bond between Jame and Tori to neutralise an overdose of Wyrm's Venom Jame had received. At the time, Jame was in the Master's House in Perimal Darkling wearing the cloak, while Kindrie was with Tori and the Kencyr host en route to the Battle of the Cataracts.
The Cloak was given to Jame by a group of "shadowy" and "golden-eyed" beings, when they send her to Gerridon's bed. They drape the cloak over Jame's shoulder saying "A present, child. An heirloom full of life!" 
↑God Stalk, Book II: Crown of Nights, "Chapter 7: The Feast of Fools" — " 'Flee, man, flee, and we will follow.' And so he fled, Cloak, Knife and Book abandoning, into the new world."
↑Seeker's Mask, "Part I", VI — "The Book, the Ivory Knife, and the Serpent-skin Cloak—those three object of great if ambiguous power kept by the Master in Perimal Darkling after the Fall. No one knew what roles they might play in the final conflict, only that each was necessary."
↑Seeker's Mask, "Part VII: Wilden", IV — " 'And the third object of power… the Serpent-skin Cloak?' 'Last seen slithering back into the Master's house. It didn't seen to fancy my company.' 'No,' said Ashe, as if to herself. 'It wouldn't. Argentiel never favors Regonereth, preserver… against destroyer.' "
↑God Stalk, Book II: Crown of Nights, "Chapter 6: Water Flow, Fire Leap" — "A cloak made of black serpent skins sewn together with silver thread. They put it on her bare shoulders… heavy, heavy, and the tails, coiled together beneath her chin, twitched. She was climbing a stair. The snake heads thumped on each step at her heels."
↑Dark of the Moon, "Chapter 13: Converging Paths" — "Here, here! A present, child, an heirloom full of life! It was made of black serpent skins sewn together down two thirds of their length with silver thread. The snakes' tails, coiled together in a knot beneath her chin, twitched."