You're kidding me, right? You really don't understand that a flat tax is regressive, i.e. that it falls heavier on the poor than the rich?
Not at all. The very definition of a regressive tax is that lower incomes are taxed at a higher rate, which is not the case in a flat tax system. Now, given that, there certainly could be a partial regressive effect because of the percentage of one household's income going to necessities vs. "toys." However, I would argue that, because the "poverty" line is a political football, and that even the poor in the USA are much better off than most other citizens of planet Earth, it isn't a valid argument against a flat tax rate.
I think it's a knee-jerk reaction to presume that a flat tax would be unfair to the poor, simply because we have used progressive taxation for so long that it feels like "that's the way it should be."
Of course, such a change would be a jolt to those who haven't been paying any income tax to this point. But there is good reason to believe that everyone should pay something, IMO.
Perhaps there could, instead, be an exemption for those below some "minimum living standard", and so implement a hybrid system with two tiers: a no-tax, poverty tier, and a flat tax for the rest. At least that would reduce the current system to one political football: the "minimum living standard" line.