I hate to say it, but probably never. Or at the very least, they're going to have to invent a new kind of physics first, which could happen tomorrow but is more likely decades or centuries off.

There are two basic ways to make things fly. One is to basically swim in the air. That's what wings are for, whether it's fixed wings or rotating wings. The wing pushes against the air, giving lift. Such objects are always very tricky to fly, because air is invisible and full of currents you can't see. You need a lot of training to be a pilot in order to handle that. The actual flying part is relatively easy, but dealing with traffic is hard because you depend on your motion. You can't stop, which means planning far ahead and knowing what everybody else is doing. Any kind of traffic jam would literally kill everybody, and you can't just turn out of the way of somebody doing something unexpected. (Helicopters handle that better, but they're even more complicated.) So I just don't expect that to be something that ever becomes common.

The other path is the rocket path, using a reaction mass rather than depending on the air. Such things don't depend on your motion. Unfortunately, they also require vast amounts of energy, and they're very hot, and therefore very dangerous. They do make small jet packs, but they're very expensive and unlikely to get a whole lot cheaper, especially since the best way to fuel them is with petroleum. (It has the best weight-to-energy density of anything known.) Their range is very short, and they're actually very efficient already, which means not a lot of room for improvement.

Yes, birds can do it, but you'll notice that birds are very, very small and light. The lighter something is, the easier it is to make it fly. You are already considerably more massive than a bird, and a flying car just adds more weight. The more weight means the more fuel you have to carry, which means even MORE weight. All of this means that you're talking complicated engineering to make it work, and complicated learning to fly.

Something could come along to change this, of course, but I just don't expect flying cars to ever be common. The things you see in sci-fi movies violate the laws of physics, so unless somebody has some REALLY novel insights you won't ever see anything that moves like that.