Aromor items that are enchanted don’t have a shimmer effect when being worn by a mob or player. Only items on an inventory slot have the shimmer effect. Elytra is not affected by this bug.

How to reproduce: 

for player:

1. Wear any armor item
2. Look in 3rd Person mode at you. 

for mobs:

1. Summon a monster that can pick up loot. You can use this command :/summon minecraft:skeleton ~ ~1 ~ {CanPickUpLoot:1b}
2. Drop any enchanted item at it.

What I observed: There is no shimmer effect:

What I expected: There is a shimmer effect: