Flat Tax: Much the same. We currently have a progressive tax system -- the more you make, the more that tier of money is taxed. Everyone pays the same tax per tier, it's just that only the wealthy reach the higher tiers and pay the higher rates on them. But if you flatten that to one rate, what happens? The rate on the lower tiers that everyone is paying goes up and the rate on the upper tiers that only the wealthy is paying goes down.
Flat tax without deductions wouldn't benefit the wealthy as it's pretty well documented that dodging the wild majority of income tax is pretty trivial if you can afford a decent tax attorney and plan your compensation a few years in advance. Every flat tax proposal starts out as "just 10% of your income" turns into "well not investment income" or whatever as soon as any questions are asked. I'd lose a bunch of money if I paid 10% of my income in taxes.