If tax % are flat, the rich STILL pay more ... 10% of 10K is 1K it is also 10% of 100K. A guy making 100K would pay the the whole income of a guy making 10K in taxes. Better yet, every 10 poorer people are able to contribute as much as one rich person ... which would be a much more prevalent attitude if taxes were a shared cost of a reasonable government rather than a coercive transfer of wealth.
As I've said before, a tax cut is not a handout. It simply means government steals less. What progressives want to do is take money from some -- by force -- and spend it on others. It sounds less noble when plainly stated.