This is such an interesting question! The first thing that leaps to my mind is that privacy creates conflict, which is an element that a short story should have. I am going to provide you with a list of questions to get you thinking about how the theme of privacy can create conflict, I hope enough to get some ideas brewing in your brain.
Is there a conflict between a teenager's privacy needs and parents' need to be good parents? What kind of tension is there that could be demonstrated through characters in a story?
Is there a conflict between good friends when one person is very private and the other is very nosy? Has that ever happened to you? Can this cause a person to lose a friendship, do you think?
Is there a conflict between a girl and a boy when one of the couple wants more privacy than the other? Could characters in a story show how this can be a problem?
Is there a conflict between the government's need to know things and our privacy as citizens? What happens to people when this conflict exists that you could show in a story?
Is there a conflict between our need for privacy and the social media that we use, for example Facebook? Do people have problems when they give up their privacy? What could happen to a person whose privacy was violated?
What you want to remember is that my questions are about ideas. And in a story, you need characters who are in situations that show the reader about the theme of privacy. You will not want to tell the reader about your theme, but you will want to let the reader see the theme through the words and actions of your characters.