Welcome to Larry Page’s Secret Flying-Car Factories

Three years ago, Silicon Valley developed a fleeting infatuation with a startup called Zee.Aero. The company had set up shop right next to Google’s headquarters in Mountain View, Calif., which was curious, because Google tightly controls most of the land in the area. Then a reporter spotted patent filings showing Zee.Aero was working on a small, all-electric plane that could take off and land vertically—a flying car.

In the handful of news articles that ensued, all the startup would say was that it wasn’t affiliated with Google or any other technology company. Then it stopped answering media inquiries altogether. Employees ...