The Flamingo Hotel was originally called the Flamingo Hilton, and was owned by Hilton. When Hilton built the Flamingo HGVC, they wrote into the deed the fact that HGVC owners have the right to use the Flamingo pool. Good thing, because Hilton later sold the Flamingo Hilton, which then became just the Flamingo Hotel.
I respectfully disagree with John about the Flamingo hotel pool. Yes, it's frequently crowded. But that's because it's one of the nicest pools in LV.