Both flat tax and sales tax disproportionately tax the poor.
The very rich spend less money relative to how much they make, which puts higher burden on the poor than with our progressive tax.
Flat fax is bad, because 40% of the guy making 20k per year is going to severely change quality of like. 40% from the guy making $40 million has much less impact on his quality of life. This is the whole reason for having a progressive tax... Impact of money on quality of life doesn't work on a linear scale, so neither should our taxes.