There is a strong case for flat taxes. They reduce compliance (and avoidance) costs. They create a very broad base for taxes that in turn distort the economy less and have a lower dead weight social loss. The Economist says that they may be practical and feasible.
The conventional wisdom from (NYT, April 10) is that alternative minimum taxes (AMT) are bad news. An alternative view is that they are a back door way to get a flat tax. The number of people who pay AMT is expected to grow to $200 billion projected in 2015. This growth is due to three factors: deductions get more generous, maximum marginal rates stay low due to the tax cut, and inflation and growth steadily increase income. While $200 billion less than 5% of the federal budget and less than 1% of the $20 trillion economy (in 2000 constant dollars) projected for 2015, it is still a significant portion of taxpayers paying a flat tax.
If US wants a flat tax, it should do nothing about AMT, it should increase deductions like crazy and reduce the marginal rate of the non-flat tax further. For those worried about the budget deficit, the AMT rate can be raised, or perhaps Medicare and Social Security rationalized.