White flight in the US also wasn't about people leaving the city centers for the suburbs; it was about people leaving suburbs for other suburbs.

The postwar flight to more distant suburbs was due to WW2 veterans suddenly having way more wealth than they had pre-WW2 (i.e. during the Great Depression) and deciding they wanted an upgrade from living in a cramped, dirty, noisy city, with the meteoric rise of the automobile and marketing campaigns by developers helping out a lot as well. This flight was almost exclusively white, but it wasn't motivated by a desire to get away from black people, andd the only reason black people didn't join them was because of systematic racism gatekeeping them out of the new developments. Restrictive deed covenants imposed by developers, banks refusing to do businesses with people whose addresses are in black communities (most commonly known as redlining), and just plain old institutional poverty kept black people out of something that all Americans wanted to participate in.

Also keep in mind that suburbs weren't nonexistent pre-WW2 either; these old suburbs were transit-oriented and are now referred to as "streetcar suburbs". Pretty much every city in the US has a number of inner suburbs, just outside the central business district, that consist of single-family homes on an oblong grid of streets with alleyways and the occasional arterial (which originally contained a streetcar line) dividing the neighborhood (if anyone reading this has no idea what I'm talking about, let me know and I'll post Google Maps links). What was different about postwar suburbs is that they were much farther away from the city center and were car-centric in their design.

White flight was a later phenomenon that resulted from the civil rights movement dismantling a lot of racist institutions, causing white people to freak out and leave the suburbs they moved to following WW2 for other suburbs. Restrictive deed covenants and redlining were banned, black people finally being able to both move into any neighborhood and access mortgages, so of course they moved out to the suburbs. And then the white people fled. This is why much of the original postwar suburbs are now considered "the ghetto" (for example, Wynnewood was built as Dallas's version of Levittown, the whitest postwar suburb you could imagine, but is now majority black and Hispanic, and the name of the larger part of town it's located in, Oak Cliff, is almost used as a slur by racist white people). Black people moved in, racist white people moved out. Exploitative race-baiting real-estate agents even deliberately encouraged this phenomenon to buy low and sell high, a practice known as "block busting", which is now also banned. The agents would buy up a house in a white neighborhood and both sell it to a black person and send agents provocateur to talk to all the existing residents and stoke fears of black people moving in en masse. They would even hire black people to push baby carriages throughout the neighborhood! And so all the white people would sell their houses and move away ASAP, and because they decided they wanted to get out right now, they sold cheap. And the block busters bought up the houses and turned around and sold them at exorbitant prices to black people wanting to move to the suburbs for the first time. In Chicago, for example, block busting was so widespread that which suburbs were considered "white" and which suburbs were considered "black" would change every few months, as people would play racial musical chairs to a beat set by unethical salesmen.

Interestingly enough, many cities are now at a point where things have settled into a new mix: inner-ring suburbs are often very diverse, while the exurbs are extremely white. As PoC move farther out, white people build entirely new neighborhoods even farther out. My own experience in Dallas is that as the exurbs grow even farther and farther away from the city, more and more neighborhoods in the inner suburbs are becoming Chinatowns and Koreatowns (and as someone who lives in the inner suburbs and has diverse taste in food, I welcome this phenomenon).