You can't put elytra on armor stands even though dispensers do place elytra on armor stands.
Code analysis by marcono1234 can be found in this comment
elyctra cant be put on armorstand back
It is not possible to place Elytra in armor Stand
Armorstands don't display elytra
Armourstands can't wear Elytra
elytra cannot be equipped onto armour stands
Elytra not rendered on entities/mobs