The problem is that sales taxes are inherently regressive, not flat.
It sounds ridiculous, I know. But - if you live paycheck-to-paycheck, then by definition, you're spending all of your money buying things. If you have income high enough that you're putting away savings, then you spend a smaller fraction of your money - and thus a smaller fraction of your money is subject to the sales tax.
Therefore, a nominally flat sales tax actually taxes the poor more harshly, percentage-wise, because the poor find it necessary to spend a larger fraction of their money. Same logic applies to almost all consumption taxes, save specific luxury taxes (which I disapprove of on entirely different grounds).