The Xbox 360 Edition (TU73 / Legacy Console Edition, final update 2018) does not have Elytra (wings). Flight is only possible in Creative Mode.
If your Xbox 360 Edition is fully updated (TU73, 2018), you have Elytra. If playing offline on old TU, you may not. Check for "Elytra" in Creative inventory (Combat tab).
Mods are not possible on Xbox 360 (unsigned code blocked). PC Java/Bedrock editions have full mod support for flight mods.