Yes, I would support a flat tax.
On the one hand, on the lower end of the spectrum, those who are not currently paying anything would then be paying something, albeit not a whole lot. This would be positive, in that it heads off the tendency for those on the lower end of the spectrum to vote for "bread and circuses" types of wealth transfer programs -- the sort that has doomed democracies and republics since that sort of government first came about so long ago. By making it clear that they do have some stake in keeping costs under control, they are that much less likely to want to vote themselves largesse from the public treasury, and that much more likely to want to get rid of the politicians who try to buy their votes with the taxpayers' (now, their own) money with socialistic schemes.
On the other hand, a flat tax does away with the legal loopholes that allow the super-rich to avoid paying much in the way of taxes at all (which is repugnant), all the while lowering the top tier marginal tax rate to something reasonable -- since the net effect of high marginal taxes is the drying up of investment capital: investment capital that provides the impetus for new business startups, business expansion, etc. All of which means that high marginal taxes mean less new jobs for everybody.
Those in the middle remain largely unaffected.
I, for one, consider a flat tax (perhaps, or maybe preferrably, a sales tax on consumption) to be a fair tax.