Here's all you need to know about these taxes the flat tax on incomes or on consumption: they're regressive. They fall much harder on middle and low income people than on the rich "for the simple reason that most lower income people use all of their income to pay for food, clothing, shelter and other consumption whereas members of the upper class have lots of cash to spare that they are unlikely ever to consume in their lifetimes. There are additional significant flaws in those tax schemes, like unrealistic economic assumptions, difficult transition paths, rosy revenue scenarios, misleading propaganda about rates and the probability that a national sales tax that cuts deeply into lower income finances will repress consumption that fuels small businesses." And they would join a lot of other regressive taxes already out there: state and municipal sales taxes, for example.
There's a really good discussion of why these tax proposals are good only for the uber rich right and why the Cain plan is even more regressive here.