Symbol of the office of Sorcerer Supreme, the cloak permits the Sorcerer to fly. The cloak has a mind of it’s own and will only permit it’s chosen appropriate use.
The Cloak of Levitation is one of Doctor Strange's most prominent parts of his attire and equipment. The cloak was gifted to Strange by the Ancient One after prevailing in battle against Dormammu. It was soon destroyed by the monster Zom in combat with Strange, but Strange skillfully restored it soon afterwards in a feat that impressed the Living Tribunal.
During the Empirikul's attack on magic and Doctor Strange's defeat, the Cloak was torn apart by the Empirikul's leader, the Imperator. When Strange managed to be teleported away to safety, he retained a shred of the Cloak, which barely retained its magical properties and couldn't even fly.
Flight- The Cloak of Levitation grants it’s user the ability to float and fly, in a much more effective way than using a flight spell. The Cloak of Levitation unable to be controlled. It's also possible to use the Cloak while standing on it, in a similar way to a magic carpet. Additionally, the Cloak responds to commands and can be directed even if not being worn.
Extra Limbs- The Cloak can also be used as shield, because of it's durability, offering the wearer some protection or as a weapon, due to its ability to ensnare opponents It can also alter its shape, being capable of grabbing onto ledges.
Mystic Arms: Extra Limbs 2, Sustained Enhanced Dodge 2, Sustained Enhanced Parry 2, Sustained Reach Move Object 18
Comic Vine: Cloak of Levitation article- https://comicvine.gamespot.com/cloak-of-levitation/4055-56046/
Marvel Database: Cloak of Levitation Article- http://marvel.wikia.com/wiki/Cloak_of_Levitation