A flat tax would be great if we were all communists. In a capitalist system money makes money.
If you earn 100k and pay 20k tax, 50k expenses, you have 30k left. Say it's invested @10%, next year you earn 103k. If you earn 200k and pay twice as much tax (no progressive tax system is that punitive btw), you have 110k left. Next year you earn 211k. After three years, your relative tax burden is
lower than the guy making 100k, and shrinking. That's an oversimplification due to capital gains taxes of course, it actually takes a little longer
Worth noting is that fluctuating investment returns only have a short term effect. You will never lose in the long run unless the entire system completely collapses. Risk vs reward does not apply to diversified investing in a stable economy, even if you put all your money in startups, and the only criteria for stable here is 'will be around longer than you'.
Against that I'm not sure what the argument in favour of a flat tax is. The wealthier you are, the less tax you pay relative to that. Progressive tax systems are designed to counter that effect somewhat, not completely, in order to maintain that social mobility I mentioned. Without them, your entire economy decays. The only other way to stop all the wealth slowly gathering to fewer and fewer people (eventually reaching one, who pays everyone else a subsistence wage) is 100% capital gains tax, which obviously doesn't work.