When using this command to spawn a Zombie with the Elytra equipped in the Chest slot, two things occur:
summon Zombie ~ ~1 ~ {ArmorItems:[0:{},1:{},2:

,3:{}]}

The zombie wont render the Elytra Item at all, like it isn't there, but is still fully functional. This effects all mobs.

When the Zombie is also flying the elytra, he doesn't do the animations he should with the item. He continues to stand up and move erratically when pathing towards the player.