This is the first year that I've heard of this chumra of not eating flour that was ground before Pesach and sold. Presumably, this chumra only applies in Israel, where the vast majority of flour stocked in stores and warehouses is owned by Jews. The ostensible reason for this chumra is a concern that a) the flour came into contact with water and became chametz, and b) the sale of chametz to a non-Jew is not a truly valid sale.
The reason that this is not a concern is:
1) Chametz that was owned by a Jew during Pesach (Chametz she-avar alav ha-Pesach) is forbidden by rabbinic injunction (mi-drabanan). Since there is no certainty that the flour ever came into contact with water and, indeed, it is likely that it never did, the issue becomes, at the very worst, a 'safek de-rabanan' (doubt in a case of rabbinic injunction), which the halakha treats leniently.
2) Since flour is generally sold along with the chametz, and was not owned by a Jew on Pesach, there is no reason to be machmir. Even those who do not personally sell their chametz because they find the sale to be dubious do not consider chametz that was sold to be "chametz she-avar alav ha-Pesach". This is because there is a long-standing tradition, upheld by major halakhic decisors, of selling chametz to a non-Jew. The rabbinic injunction against "chametz she-avar alav ha-pesach" would not apply in cases where the alleged "owner" of the chametz relied on an accepted mechanism for obviating that ownership. I.e., even though Person A might not accept this mechanism, he need not - and should not - consider Person B to have violated the laws governing chametz ownership on Pesach by availing himself or herself of that mechanism.
Please note that each of these 2 reasons operate independently and is sufficient to undermine the practice of insisting on flour that was ground after Pesach.
[Here's a question that may be relevant, and I simply do not know the answer: do we employ bittul be-shishim with regard to chametz she-avar alav ha-Pesach? If we do, then there's another reason not to be concerned].
My final reason is sociological: this chumra is almost impossible to apply consistently. There is no way that the chametz products that hit the shelves after Pesach were not sold. One would have to wait several weeks before consuming chametz products if one were to take this chumra to its logical conclusion. If would apply all year to chametz products - beer and liquor come to mind - that have a longer shelf-life. You may as well stop going to shalom zachars.
This chumra definitely goes into the "close to apikorsus" and "idiotic" file. See here.