Nekhii received her Echo the canonical way: A vision of a meteor shower while she napped on the cart into Gridania. In addition to the visions of people’s pasts and understanding of other languages, her Echo also lets other people understand her when she uses sign language, since she doesn’t speak out loud prior to ~level 68-ish in Stormblood (and can be rendered mute by stress even after that).
She also got an upgrade of sorts in the Praetorium when she and her co-WOL, Carmein, used their Blades of Light to banish Lahabrea. The blades touched, connecting their souls and reawakening a soulbond they had in their past lives as Azem (Carmein) and Hythlodaeus (Nekhii). This isn’t exactly “the Echo” but they assume it is for a while. They can communicate telepathically and sense each other’s emotions. (Emet-Selch is also included in this, but he is able to shut himself off from them because he actually knows what he’s doing. It might or might not be a coincidence that “Emperor Solus” died right after the WOLs unlocked their soulbond.)
Also! Not knowing any better, she attributes her her soul-sight to the Echo. She has no idea what it is until shade!Hythlodaeus explains it in Amaurot, just thinking there’s weird auras around people sometimes and the colors never repeat, except when they do (Carmein and Ardbert).