I have ran the dust palace over 10 times today with different groups and not one person has received a flayer mantle or treads upon stars. Also the loot which should be dropping as engrams directly on the ground post kill are simply appearing as on screen rewards. I am seeing many other posts on which the same issue is being described. I have been waiting a long time for this nightfall to farm the cloaks and would really like for this to get fixed.... I hope to hear something from a mod or Bungie official. Thanks...
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Bungie has already stated that there is an issue with Strike specific loot dropping for the Dust Palace. Once the issue is correct then we'll be able to farm it. Until then, it's worth it for the rep if you want it, but I wouldn't run it until it's been fixed.