I sort of want to outsource this post to Dana Goldstein, but white parents fleeing pockets of poverty is not an argument for school vouchers. What they're fleeing is the poverty -- which, at a certain density, dissolves just about any school. If everyone had a voucher, there would still be concentrated poverty in DC, and thus in its schools, and white parents would still move away so they could easily send their kids to other schools. What they're seeking is economic segregation, not school choice. And the way you achieve that is move away from poor areas. Which is something that school vouchers would not, sadly, allow poor families to do.
Of course, this argument would fall apart if voucher experiment had actually been shown to improve student scores. But that hasn't happened. In fact, it hasn't happened multiple times. But don't get me wrong: I take very serious the inequity of rich families just wandering off from pockets of poverty, leaving the areas all the worse off for their increasing economic homogeneity. So I support a broad range of economic integration measures, ranging from housing vouchers to legislating integration into appropriate school districts. But school vouchers don't show much hope as the answer to that problem.
Incidentally, Greg Anrig has a terrific chapter on the disappointing results of the voucher and charter experiments in his new book, which you should all buy.