The flat tax won't work for several reasons. First, it keeps the income tax in the law and would not get rid of the IRS. Second, the complexity comes in determining what deductions are permitted, not in the tax rate. If deductions are "simplified" to one size fits all, then businesses will be hurt badly by being unable to deduct reasonable expenses of doing business.
Didn't our current tax mess originate from a "flat tax"? If so, I see the flat taxers as just being willing to hit "ctrl-alt-delet".