This article is old, but it contains a helpful segment in what is a good overall argument in favor of the flat tax. Consider:
Once tax codes have degenerated to the extent they have in most rich countries, laden with so many breaks and exceptions that they retain nothing of their original shape, even the pretence of any interior logic can be dispensed with. No tax break is too narrow, too squalid, too funny, to be excluded on those grounds: everybody is at it, so why not join in? At the other extreme, the simpler the system, the more such manoeuvres offend, and the easier it is to retain the simplicity.
Believing that it will be easier to retain simplicity might be a smidge optimistic, at least for the United States, but the idea is defensible. What’s important is that we achieve intelligent tax reform. The tax code needs to be simple. The quickest way to understand the correct path is to realize that the tax code cannot be used to create growth without picking winners and losers. Reform should seek to destroy as little economic incentive as possible. It should let merit and effort create favorable outcomes.