Does Fading Memories count as killing a unit with a spell so I can cast Immortal Phoenix?

No, Fading Memories does not count as killing a unit with a spell for the purposes of triggering Immortal Phoenix.

According to RiftJudge FAQ #1453 and FAQ #6316:

• Fading Memories is not a "kill spell." It grants the Temporary keyword to a target.
• The unit dies due to the Temporary keyword, not because of a "Kill" instruction or damage dealt by the spell.
• Because the spell itself is not responsible for the kill action, it does not satisfy the condition "When you kill a unit with a spell" required by Immortal Phoenix.