No it doesn't. Those with less to spend also spend less.

Contrary to popular belief, the so called utopias like Sweden, tax the poor at almost comparable rates as the rich.

Those who earn less pay less in income tax and we still had to implement a progressive taxation policy because of how much a flat tax percentage hurts those without disposable income compared to the wealthy.

The poor already spend all their money on necessities. If you go to a flat sales tax it will hurt them more than the current progressive regime and favor the wealthy.

You can exclude necessities from sales taxes and alleviate most of the taxes paid by the poor.