Trouble with a flat tax system is the poor can't afford the tax rates the nation's current expenditure would require. It would work O.K. if the expenditure was much lower, but I see no way to get from here to there.
Aside from that, I've come to believe that a flat tax system isn't actually fair. The less income someone has, the more taxes cut into basic living expenses (because a greater portion of that person's income is spent on basic needs). On the other hand, someone with large incomes sees no tightening of basic living expenses because they make enough that the money lost to taxes falls solidly into the "extra income" region.
I'm not very good at describing this idea yet, but I tie it back to the idea I have happened upon that (for example) a 25% raise to a person making $40k is in terms of spending power much more than a 25% raise. This is because discretionary income is much smaller than $40k. The new $10k can be considered added discretionary income (assuming the person was meeting basic needs before) thus making it in effect much larger than a 25% bump.