There are two completely unrelated kinds of flying car.
First is the Jetsons version of the flying car. This is the aviating equivalent of the personal automobile. You get in, you fly it to work from your driveway, land it on the roof of your office building, and walk in.
Second is what this was: a machine that's both a road car and an airplane.
The first one is at least conceptually very neat. If it worked, it could completely eliminate traffic jams, eliminate pedestrian-vehicle accidents, and vastly improve the efficiency of local transport. There's been little attempt to build such a thing. It basically demands VTOL operation, which vastly restricts its range and increases its cost and noise. The Moller Skycar is the only real-world attempt at this one that I can think of, and it didn't get very far.
The second one is completely pointless. The "flying car" as it actually (barely) exists, as in this example, is just a car that is also an airplane. You drive it to an airport, reconfigure it to be an airplane, fly it to another airport, land, reconfigure it to be a car, and drive off.
The problem is that design tradeoffs mean that such a "flying car" is both a bad car and a bad airplane. They have inherently different needs for things like wheels, engines, drivetrains, etc. Putting both into the same machine means it's not going to do either one well.
For every "flying car" out there, you can take the same money and buy a better car, a better airplane, a second better car to keep at your most frequently used destination airport, and have enough money left over to rent cars at other airports for years and years. This is unlikely ever to change.
The Jetsons idea is interesting, but roughly nobody is working on anything at all applicable to it.