When I type the command /summon Zombie ~ ~32 ~ {ArmorItems:[{},{},{id:elytra},{}],FallFlying:1} in 1.11.2, 1.11.1, and 1.11, it doesn't work. However, if you type this command in 1.10.2, it works normally.
Just to double check, I did /summon Zombie ~ ~32 ~ {ArmorItems:[{},{},{id:"minecraft:elytra"},{}],FallFlying:1b} and /summon Zombie ~ ~32 ~ {ArmorItems:[{},{},{id:"minecraft:elytra"},{}],FallFlying:1s} and they also didn't work so I'm sure it isn't an error in my command.
All items need a Count of at least 1, yours is null-> 0.