Kiki is an adorable nn. I had a friend named
Kirsten. Her little brother couldn't say it and called her
Kiki.
Here's my theory on nns. They don't have to bear any logical connection to a name. Their primary purpose is to show endearment. Therefore, they are the best place to let whimsy, imagination and emotion soar. The formal name is the name to make a good first impression with. The nn is the place to lavish affection.
So sure --
Kelsey Claire, nn
Kiki, makes perfect sense to me.