He's wrong for a variety of issues in this - he shows a profound lack of understanding of the changing economic conditions within the United States (embarrassing considering he's an economist), the shift in urban political design and zoning, the barrier to entry regarding the opening up of physical stores, and the reasoning behind the rioting that was claimed as the end to easily-accessible stores.
Harlem was indeed bereft of quality stores at the time, people in Harlem during Sowell's childhood (the majority of whom were Black and white migrants) both grew and cultivated their own food to handle dry seasons in the stores, and received a steady shipment of produce and other necessary products from family members, friends, and neighbors - a good amount of which came from out of the area.
Food at the time was marked up in Black communities and Black neighborhoods (the same was true of rent, even in substandard conditions, Robin DG Kelley, Manning Marable, Keeanga Yahmatta Taylor, and Isabel Wilkerson all note this in their books, Hammer & Hoe, How Capitalism Underdeveloped Black America, Race for Profit, and The Warmth of Other Suns, respectively), but local production and smaller stores were a national thing - both in white neighborhoods and black neighborhoods - not *just* a product of segregation, but a product of the local mode of production and supply chains.
There's a reason he jumps from anecdotes to data, because his conclusions tend to be baseless.
Riots did not lead to white flight, but were in fact explicitly a product of white flight - the subjugation and exploitation that was openly visible and was happening as suburban sprawl commenced - was what led to these uprisings. "Race riots" having been a regular occurrence in the U.S. since the end of slavery (and largely before that, W.E.B. Du Bois notes it a few times in Black Reconstruction, but these anti-Black pogroms against free Blacks were not new). The poorest and most exploited areas were often in close proximity to working-class white neighborhoods, and the poverty simply continued after the end of the era - not as a product of uprisings during that era but instead due to wealth reproduction and the continued austerity and wealth extractive policies of a given local, state, and federal administration.
He also ignores the mass proliferation of Black businesses that came about throughout the 20th century, even as financial institutions either explicitly tried to undermine them, or lent to them at absurdly higher interest rates; the difficulty in maintaining stores in poorer neighborhoods due to issues of credit and access, as well as the clear problem of racial and economic segregation making a lower-income population the default customer base.
All to say: Sowell is an ahistorical clown who has no idea what he's talking about.