How would a flat tax policy curb income inequality? We have a progressive tax system right now, yet the wealth gap has only increased.
Preventing the an increase in the wealth gap is a difficult proposition no matter what taxation system is employed. Fundamentally, I'm unconcerned with the exact magnitude of the wealth gap. There is in an ideal sense nothing implicitly good about income equality if the total wealth being divided is too low. In the United States, this is not the problem, with a GDP per Capita of $53,041.98 (2013).1 But before one speaks of redistribution, one ought to consider why that wealth is so high, and whether redistributing that wealth to less productive citizens will have a positive or negative impact on the generation of wealth. Furthermore, I am not altogether comfortable with confiscating what other people have earned.
The real issue is whether the mean wage among low earners is sufficient to live a good life and encourage the spending required to sustain an industrial economy. This is best achieved by the progress of technology and the maintenance of low prices on goods, which are multivariable functions that seem to operate best under conditions which tend toward a free market, with some public-private partnerships (as in the case of public research and education).
So to answer your question, it is not my intention to solve income inequality by a flat tax. If one wishes to solve the bad aspects of inequality then there are a few promising avenues that I would hazard might be effective. First, the federal government must stop enforcing the monopolies of a select few companies by subsidies and preferential legislation. This phenomenon can be observed quite easily in the telecommunications industry. The United States has robust Anti-Trust laws, but the last time they were employed to significant effect against that industry was 1974.2
It might also help to target regional, as opposed to personal income inequality. There is a compelling body of evidence which suggests that regional income inequality (between, for example, New York and Ohio), has a significant negative impact on the growth of the national wealth.3|4|5