Flying cars are a wildly impractical way to get people from one place to another.
The question assumes that both technology and our standard of living will increase to the point where such a inefficient mode of transportation will be feasible.
More likely we will use telepresence rather than physical transportation for a lot more and the few things we have to physically be someplace we will use high efficiency surface transportation.
I don't think you anyone needs to worry about for a long time, I can't picture flying cars being main stream for a few hundred years or so, long after you and I are gone.
I have seen some flying car pictures in internet and i feel these will be introduced into the world pretty soon for sure and may not take 100 years as you said.