On an actual PSP, the "Download List" section of the PlayStation Store may still function for re-downloading previously owned items if you can connect to a compatible Wi-Fi network (typically requires a 2.4GHz "Open" or WEP hotspot).
However, there’s a critical catch for modern players: You cannot purchase or download these DLC packs through conventional storefronts anymore. dissidia 012 duodecim final fantasy dlc pack download