I've almost completed unlocking the DJ Station portion of KOFXV, so I thought I'd share the list of how to unlock each of the different playlists. With the Destiny Battle list you can just go into training mode and select the characters/stages required, just make sure that the BGM is set to default or it won't unlock.
Complete story mode with these team edit teams, most have ending scenes but a few do not.
SNK: Athena, Clark, Ralf.
Neo Geo: Kyo, Terry, Ryo.
Fatal Fury: Terry, Andy, Shun-ei
Metal Slug: Heidern, Clark, Ralf.
Samurai Shodown: Ralf, Maxima, Antonov.
KOF95: Dolores, Terry, Vanessa
KOF96: Mai, Luong, Chizuru.
KOF97: Leona, Iori, Shun-ei.
KOF98: Benimaru, Yashiro, Robert.
KOF99: Meitenkun, Chris, KulaKOF00: Ramon, Angel, King of Dinosaurs.
KOF01: Ryo, Krohnen, Angel
KOF02: Dolores, King of Dinosaurs, Clark,
KOF03: Yuri, Athena, Isla.
KOFXI: Isla, K', Krohnen.
KOFXII: Kyo, Ash, K'.
KOFXIII: Elisabeth, King, Shermie.
Destiny Battle KOFXV BGM (can be unlocked in training mode):
Ash vs Elisabeth : No.53
Mai vs Andy: Club M
Kyo vs Iori: Sadistic Eyes
Iori vs Kyo: Goodbye Esaka
K' vs Krohnen: KD-0084
Yashiro vs Iori: Bloody
Shun-ei vs Meitenkun: Sobagaramakura
Dolores vs Kukri: Sand and Mud
Clark vs Ralf: Storm of Cheers
Antonov - Hyper Galaxy Ring: I was the King of Fighters
Athena - Concert Hall: Psycho Soldier 2018