In the language Tagalog, Philippines, it means vagina. I learned this from my Filipino friend when I lived in San Francisco many years ago. I also checked several Websites. I've called my son Kiki since he was a baby. It's a pet name for him, not used around people outside our family. This was true even before I learned the Tagalog meaning. :)
I know a lady named Vasiliki who is called Kiki. She is Greek-American and accents the nickname on the first syllable. I don't know if this nickname would be used for this name in Greece.
The name is very pretty. I live in Croatia and Kiki is used in Croatia as a nickname for Kristijan (Christian) so there is a lot of Kikis in Croatia (my dad too, but his name is Dragan). In Croatia the nickname for Kristijan is not Chris or Cris.