No serious reputable anything has ever found a flat tax to be anything but a huge giveaway to the rich as well.
Just fund the IRS and stop letting the foxes run the hun house, ie. get money out of politics and stop letting a few people and their rich friends make all the rules to favor that small cadre.
You might as well tell people to make other people stop being corrupt. Humans are corruptible full stop. For a funny recent example see Russel Brand's last YouTube video on the US Congress's insider trading clown shows, and then ask yourself if there's any way possible to get this legislative body to "stop letting a few rich people and their rich friends make all the rules to favor that small cadre."
The only decent solution would be a vastly simpler system with enough transparency and accountability the average person could make sense of it.
We don't punish white collar crime for the same reasons. If you made it illegal to get outside money for politicians, and made the punishment significant, the rats would scurry and "normal" people could get involved in the process. The way it works now we just get rich people looking after rich people problems because theres no way to overcome all the money flowing around with any regular success.
We can try to change government, but do a quick thought experiment: how many resources does it take to manage shared infrastructure and services for 20 people? 200? 2000? 20,000? 200,000? 2,000,000?
Go on up to 350mil.
It's not easy, and you can't just "tear it down". You can envision some ways to streamline some things, but the problem is just mind boggling gigantic.
Just fund the IRS and stop letting the foxes run the hun house, ie. get money out of politics and stop letting a few people and their rich friends make all the rules to favor that small cadre.