What is the difference between "Ki kote" and "kote"?

No difference. "kote" is a contracted form or short version of "ki kote" which means "where".
See the examples below and see the following link on WHERE

Ki kote ou prale?

Kote ou prale?

Where are you going?

Ki kote ou te jwenn li?

Kote ou te jwenn li?

Where did you find it?

Mwen pa konn kote li ye.

Mwen pa konn ki kote li ye.

I don't know where it is.

kote as a noun means place, location, somewhere, etc..

Mwen prale yon kote.

I'm going somewhere.

Mwen te sere li nan yon kote ki sekrè.

I hid it in a secret location.

Ask me anything