flat-tax also increase inequalities:
1000$ a month with a 20% tax: you already have difficulty to pay for your food, goods, appartment
10000$ a month with a 20% tax: you have no difficulty to live
In some countries, you have a progressive system:
poor : no tax
lower class: small percentage
midle : normal
high: high percentage
So everyone can live without being strangled.
Take a look at poverty rate in some liberal countries with the flat-tax.
I don't believe you should pay income taxes unless you earn over a certain amount. The poor and those on part time / minimum wage would not pay any taxes. They would also get cuts on other things, like the poor already do. The tax brackets you suggested is what happens in most countries and is only fair if the percentages are fair. No tax brackets/system will ever be perfect, but I don't agree with millionaires having to pay 70% like in some countries; that's just ridiculous and complete robbery.