Richard Epstein has an article arguing for a flat tax on two grounds. First, progressive taxes generate wasteful tax avoidance. If you've ever talked to someone in asset management for wealthy people you'll know that the most pressing issues have nothing to do with picking good pre-tax investments, because moving income across time or some artificial category has a much bigger after-tax return. Secondly, when taxes are shared pro-rata the discussion on the size of government is more rational because everyone internalizes the cost. Currently only half of working Americans pay income taxes and so don't have to consider the tax effects on their income.
These are good arguments, but I'd add the following. James Mirrlees won a Nobel prize for his work on optimal taxes (see his seminal 1971 paper, An Exploration in the Theory of Optimum Income Taxation). In these models the optimal tax rates depend on assumptions about the distribution of income earning ability, the rate at which the marginal utility of income declines, and how much the tax rate deters income producing.
It is easy to see the utilitarian argument for progressive taxation: rich people don't value $1 as much as the poor, so they should be taxed more on that final dollar, but there is a powerful countervailing force which is less obvious. Given income earning opportunities are lognormally distributed, the highest earners generate much more wealth than the middle income earners. Thus, under most parameterizations you find that lower tax rates on the high earners are better because these earners are wealth-producing machines. Higher tax rates on the most productive people affects these people first, which is the exact opposite of what you want, which is to affect them the least--as far as maximizing total wealth created.
I find this literature compelling because I'm a libertarian, which is really just a dynamic utilitarian: I like to count up happiness over time in a world where people choose their actions in anticipation of certain payoffs, unlike simple utilitarians that assume output is given. Further, we tend to take for granted the unintended benefits of wealth in terms of science, art, and general human camaraderie; Marx's 'idiocy of rural life' comes from never having time to think.
Unfortunately, I think the problem is worsened by the practical fact that people are more concerned with relative than absolute income; we are more envious than we are greedy. It is a hard thing for most people, especially intellectuals, to acknowledge benefits from their rich moral inferiors who never so intended it, people who seem to enjoy it without any sense of extra obligation. Such 'progressives' see progressive tax rates as a good thing no matter how much wealth is destroyed because preventing one dollar more going to the Koch brothers is worth $10 dollars less going to a bunch of working stiffs, especially because these stiffs would probably in some way be doing business with such a bastard.
This is why the Mirrlees model is now so quaint. No one really cares about quantifying the trade-off in wealth vs. equality, because for people who care about relative wealth, aggregate wealth doesn’t matter, and what drives their confabulations is bringing down those above them (see above). No one wants to look at trade-offs because admitting there is one highlights the fiscal multipler isn’t greater than one. Better to focus on aggregate GDP, which assumes government spending and investment are perfect substitutes, and argue about the multiplier in the context of insufficient aggregate demand, a fancy both defensible and sterile.
Envy, while natural, is a vice to rise above and not a virtue to celebrate under the pretext of equality and justice.