Currently you cannot equip the Soul Elytra in the Cape slot, like you can with the vanilla Elytra. Not sure if this is intended but my suggestion is to have it also equipable in the Cape slot, especially as this is an end-game item, after killing the warden and all the Deeper and Darker mobs.
Thanks for taking it into consideration, also please let me know if this is configurable by you or the mod author.

This would be on the mod author to add compat with Trinkets API

KyaniteMods/DeeperAndDarker#106 made an issue on the mod page