First of all, I think it's important to note, like the reply article did, that the problem with the tax code is not percentages, but income calculation. The flat tax seems to be a "simplification" of the code, but it's not at all.
When Russia switched over in 2001, conservatives essentially had a giant collective orgasm, because revenues rose 5% that year (
http://www.nationalreview.com/murdoc...ck030102.shtml). However, Russia's success came primarily from the fact that before the flat tax was instituted, it had a terribly system, where oftentimes the very wealthy paid absolutely nothing. What Putin did to help the economy was cut down on loopholes and favoritism. While conservatives here took this as proof of the system's success, it hardly was. In the U.S. it's different, as while we have loopholes etc., we still have a system that the wealthy have trouble avoiding.
The problems with our system revolve around loopholes (especially with businesses, which recently were found to be paying far less than should be their share - I'll see if I can dig up the article).
I don't want to get into economics too heavily, as I'm honestly not knowledgeable enough to debate with someone who really knows their stuff. I just believe that the flat tax doesn't properly address what are actually the shortcomings of our code.