My dad served on the USS Kitty Hawk as part of a photointelligence detachment during the Vietnam War. (He served 1964-68). Even though he was not officially "ships company", would he be eligible to join the association?

According to the application form any person or their spouse who has ever served aboard at anytime or any branch of the service. So the answer is yes.

Charles,
As you now know, your Dad is now a member of the USS Kitty Hawk Veterans Association. Thank you for recognizing him for his service to our country and sharing his story with his shipmates.
Chuck Peterson