Klyros have extremely light bones/body tissue, which prevents them from wearing heavy armor, though to effectively fly like a bird they would need wings some several times bigger and stronger then they are, but using them to glide horizontally is plausible.
Also, there is a spell to weigh characters down, logically there would be a spell to make them lighter as well, and this would probably allow a klyros to flap his wings and fly upwards
Personally I'd like it if they had large bat wings which worked perfectly, seeing as we're all going to have flying bat/reptile mounts in this "far future version of the game" then it's perfectly ok for there to be one race that can fly unaided