Would a stork bite at the nape of the neck have any relation to chiari malformation?

Not unless the stork: ...was able to drill a hole into the spinal column, use his beak to grab your spinal cord below the foramen magnum & pull down 1 cm just far enough to cause a Chiari instead of killing you. Alternatively, he could've drilled into the spinal canal & sucked out 1/3 of your fluid so your cerebellar tonsils could be vacuumed through the foramen magnum. Otherwise, grievance to Mother Nature to be sent