Even if it works exactly like that, let's say you are poor and barely make enough to live, you still have to give 20% (as an example) to the government, even if you are fucked after and can't pay rent or buy food. If you make 20% more than you need, you end up with nothing left after. Rich people may end up paying more, sure, but a flat tax still screws over the poor as a rule unless there is some provision that it only starts after X income, and you know that threshold will always be set too low.

The rich also have a hell of a lot more to tax. They SHOULD be paying a higher percentage of their wealth in taxes because they've gotten a much greater benefit out of the services those taxes pay for than a poor person.