Here is the story:
I have done the Dusk Palace strike many times in the past weeks. Level 36 playlist and heroic playlist. Never got a Flayer mantle. It was frustrating.
A forum member gave me the tip to try farming the nightfall strike for the mantles. He said he got 2 mantles out of 4 nightfall completions. The first 3 times I didn't get one (done with each class), the 4th time, with my Warlock, I got the arc Flayer mantle.
I recommend farming this nightfall strike if you want a Psion Flayer mantle. Seems the Flayers are generous this week. Good luck.
Edit: Of course I don't know if the drop rate actually is higher on nightfall. But after trying to get a Flayer mantle for weeks without success on 36 and heroic playlist and now getting one after my 4th nightfall this week, I do think they are higher. If your RNG luck would suck ass like mine, you would probably think the same. Also I got 3 Treads Upon Stars from 4 nightfalls. Anyways, worth giving it a try if you've tried to get a Flayer mantle without success in the past days and weeks.
Edit 2: After another ~8 nightfall strikes I got the void Flayer mantle.
Edit 3: After another 5 nightfall strikes I got the solar Flayer mantle.
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I got solar first try. I didn't want a mantle. >_>