I'm with Cheshire Figment. It will not solve the problems of being paid off the books. In fact, it would encourage it.
Example: a home day care provider. Parents using her services are encouraged to take a tax credit, meaning that the provider must report the income. She doesn't mind doing it so much because she files as a self-employed business, so she can deduct her expenses. So she reports her income, deducts the food she serves, diapers, toys purchased, and other expenses against it. Now, go to the flat tax system. The parents don't get a credit anymore, so they aren't reporting the day care providers income. Does she report it? Hmmm she went from taxable income of maybe $30/week/child to taxable income of maybe $150/week/child.
The problem with the flat tax is that you have to define income. It's easy for wage earners and for investment income. But what about someone starting a business? What about someone who is a consultant? They could be earning big bucks, but they pay huge expenses to travel to client sites. With a flat tax are they taxed on net or gross?