If I have an elytra in vanilla armor slot, the enchant does work, but putting elytra in modded slot for backpacks and so on, enchantment is not working.

Hi! What modded slots are you talking about specifically? Nature's Aura should support Curios, so if you put your Elytra in a Curios slot, it should work fine. If that's not the case, or you're talking about a different mod, please let me know!