A flat tax with a generous lower threshold would do pretty much the same thing that we do now.
There is a lower end to the progressive tax system at the moment that wouldn't change much.
The 15% that a lot of people use is way too low for what the government would need without massive spending cuts.
I seem to remember the GAO doing a study that estimated that for a flat tax to work it would have to be around 28% anyways.
The rich DO pay a higher percentage, but that is only on earned income. The capital gains tax rates of 15% means that if you have the money to invest in things that gain in value, such as stock or other such things, the "rich" can actually pay LESS in percentage terms than the middle class, with the proper tax planning.
I have been studying individual, partnership, and corporate taxation for the last year or so, and they are the hardest classes I have ever taken.
One of the big reasons that the tax code is so complex is that people are highly motivated to cheat. Every new tax has some built-in loophole.
As a future accountat, let me be clear: I hate tax law. I prefer data analysis to memorizing tax code. I would be one of the ones standing up and cheering a real simplification of it.