Whenever I read something about the phenomenon of white flight, it's always linked to things like desegregated busing, desegregated schools and stuff like that. But though they mention things like the LA or Detroit riots as reasons why white flight "increased", seldom they appear as reasons (which I'd think are pretty good reasons to move away, if you have a group of people targeting your group of people with violence).
The same happens when dealing with white flight in South Africa post-Apartheid.
So how much did it really matter? Could those riots (or in the case of SA, terrorism) be considered a probable cause for white flight? Or is it more racist propaganda than anything else?
there have been a few posts touching on "white flight" and deurbanization; they won't answer your question directly so hopefully someone else will chip in with that, but these posts will provide more context:
What happened in Detroit that made it what it is today?
What are some pivotal events in the decline of Detroit?
Was New York of the 1970s the shithole movies make it out to be?
It's worth noting that post WWII many people wanted to get out of the cities and into the new suburbs. The question that became "white flight" was who would be able to.
Black Americans would have also left the cities for the suburbs, but they were unable to in any large numbers, for they could not take advantage of the boom of the 50's, as they were not granted access to post-war loans for homes and businesses due to racist lending practices on the part of banks. Thus what either was or would have become the black middle class was undercapitalized and left behind in the cities, while the rest of the up until then separated ethnicities that had formely lived in enclave like neighborhoods, Polish, Italian, Greek, Irish etc. took out loans, joined the middle classes increased the suburbs and became white in the sense that WASPs had been the only real whites a century before.
That's not to say that after the fifities, when the suburbs were burgeoning, and industry also left for cheaper areas, and the tax base dwindled, that increased tension between those still in the cities, particularly between those who had and who didn't have, didn't further exacerbate the desire of anyone who could, to leave.
But it stands that Suburban America was built after WWII, and everyone who could have, took part, and if they could have, Black Americans would have as well, but they were prevented in doing so.
So to answer your question, in the beginning, not at all. The movement to the suburbs wasn't racial. It was financial and many groups heretofore not considered white, as in WASP, came into the polity and left the cities as well. Black America didn't drive them out, as they would have gone too had they only access to capital.