Well, almost a flat tax. Interesting piece from Citizens for Tax Justice comparing percentage of overall taxes paid to percentage of overall income earned:
Here's a table:
Of course, simply because one cohort overall pays a proportional share of income earned by the cohort does not mean that each individual within the cohort pays a proportional share, but interesting analysis nevertheless.
http://ctj.org/ctjreports/2012/04/who_pays_taxes_in_america.php
It’s often claimed that the richest Americans pay a disproportionate share of taxes while those in the bottom half pay nothing. These claims ignore the many taxes that most Americans are subject to — federal payroll taxes, federal excise taxes, state and local taxes — and focus instead on just one tax, the federal personal income tax. The other taxes are mostly regressive, meaning they take a larger share of income from a poor or middle-income family than they take from a rich family.[1]
Many Americans do not have enough income to owe federal personal income taxes, but do pay these other taxes. The federal personal income tax is a progressive tax, and the combination of this tax with the other (mostly regressive) taxes results in a tax system that is, overall, just barely progressive. Total tax obligations are, on average, fairly proportional to income.
Here's a table:

Of course, simply because one cohort overall pays a proportional share of income earned by the cohort does not mean that each individual within the cohort pays a proportional share, but interesting analysis nevertheless.
http://ctj.org/ctjreports/2012/04/who_pays_taxes_in_america.php