My team just completed an Epic Desert Perpetual Flawless run last night and discovered that the triumph is bugged. The link above is footage of the full run without audio (not sure what happened there - it must have gotten corrupted). You can see that the triumph doesn't trigger after the final rewards (about 1:13 in the video). Also, you can see the clear listed on raid report as a flawless badge (green dot with gold star) so the game must be tracking it properly. The triumph just didn't unlock. Hope this helps!