"Any flat tax calibrated to earnings from labor and capital will necessarily redistribute income to the less well off, because an individual’s share from standard public services, such as access to public highways, does not increase proportionate to his income."Jay Epstein at Hoover.org
The rest of the article is pretty good. A head tax is regressive because the same charge to rich and poor takes more of the poor's wealth away. A flat tax targets those who are better off. And even a fair tax can be corrupted by politicians if they take too much cream off the milk. At least it reduces perverse incentives and any increase in tax will come out of the pols pockets too.
Remember, all those loopholes in tax law are a feature, not a bug, giving lawmakers the power to distribute favours to lobbies.