So when I use the command:
/replaceitem entity [PlayerName] slot.armor.chest minecraft:elytra
at first, the command will tell me that I could not replace the item in my inventory, (my chest slot was empty so it's not the command)
Then after doing the command a second time, it didn't work either.

It seems like Minecraft doesn't accept the Elytra as a chest item.

[EDIT] When I tried using this scoreboard command
scoreboard players set @a hasWings 1 {ArmorItems:[{},{},

,{}]}
I never get hasWings to 1...