Vanilla Elytra Still Works
BetterEnd does not remove the vanilla End City elytra. If you already know how to raid an End City and defeat the Ender Dragon, that route is unchanged. Fly to the outer islands, find an End Ship, and take the elytra from the item frame. This is the fastest path if you just want wings.
The 
Armored Elytra
BetterEnd adds an Armored Elytra, which combines elytra flight with chestplate-level protection. To make one you need an elytra plus Aeternium armor materials — specifically the 
Aeternium Chestplate and the relevant forged plates. The exact combination is done at the 
Aeternium Anvil using the 
Aeternium Smith Hammer, the same station used for other Aeternium gear.
Practical Steps
1. Get a vanilla elytra from an End Ship.
2. Forge an Aeternium Chestplate and any extra Aeternium Forged Plates you need.
3. Bring both to an Aeternium Anvil with your Smith Hammer.
4. Combine them into the Armored Elytra.
5. Equip it in the chest slot — you keep flight and gain armor.
If you cannot find an End Ship, remember that BetterEnd's expanded End generation adds more islands, so widen your search radius before giving up.