This is a spectacularly bad idea.
The problem with a flat income tax (yes, I know this isn't a flat tax, nor even an income tax, please bear with me) is that it produces regressive taxation overall, meaning that those with lower incomes pay proportionally more than those with higher incomes. This is because income tax is not the only tax, and nearly all other taxes are regressive. Sales tax, gasoline tax, toll roads, license fees, and building permits are all examples of regressive taxes. The rich will generally spend more on these kinds of tax-bearing expenditures, but such spending does not scale proportionally with income. A CEO who makes 200 times my salary will not drive 200 times as many miles on the tollway, for example.
Property taxes are also mostly regressive. Poorer cities usually have a higher property tax rate than more affluent ones. Because their property values are lower, these cities MUST tax those properties at a higher percentage rate to meet their expenses. It's easy to have both a low tax rate and adequate revenue when you're taxing million dollar properties. The rich pay more in absolute dollars, but the middle class and poor pay a larger percentage of their income.
Social Security tax is flat up to about $113K, then becomes sharply regressive because income above that threshold is not taxed at all. Medicare tax is flat up to $200K, then drops to a lower flat rate above that.
This "Fair Tax" has the potential to be even more regressive than a flat income tax. It proposes replacing all income taxes, including capital gains and corporate income taxes, with sales taxes, but with a mechanism that they call "prebates" that would compensate for the regressiveness at lower incomes, thus producing an effectively progressive tax up to about 233K, then nearly flat from there to infinity. That is based on their own chart. However, that chart is rather deceptive because it shows the tax rate based on spending, not income. Because the wealthy tend to use much more of their income for savings and investment, taxable spending will not scale in proportion to income, making this tax regressive at higher incomes.
Looking through their faq, it appears that the expected benefit of this is the standard right-wing "faith based" economics, in which the the economy will supposedly boom if only we can reduce the tax burden on the job creators.
Don't be fooled. This scheme heavily favors corporations and the rich, and will only accelerate the rise in income disparity and shrinkage of the middle class.