I consider myself a utilitarian. To me "fair" is irrelevant. What matters is whether a flax tax would maximize the aggregate well being of society, which I doubt.
I have plenty of reasons for opposing utilitarianism, many of which have to do with deontological ethics which are related to my faith and personal morality, both of which can't really be "Proved" with any emprical framework. However,
this has always struck me as a pretty good argument against utilitarianism. This may have been refuted before, but I find it to be a pretty good argument, or at least one worth a casual debunking.
As far as my (
Deontological, based on the non-aggression principle for legality and based on divine command for morality*) ethics go, they also render this question pretty irrelevant. I consider any government that goes beyond its proper bounds to be fundamentally evil in doing so and so any tactic (That is not immoral for some other reason) that helps to right this state of affairs is ethically right. So to raise taxes on anyone when the government is clearly out of bounds would be, to me, unethical. Since it is highly unlikely that any flat tax would reduce income taxes all the way down to the taxes that the very poorest pay, any attempt to raise taxes on them would be currently unethical, as it would enable our current spending.
So, in other words, right now it would be ethical, in my view, to vote against ALL tax increases, and vote in favor of ALL cuts, at least until government is retractred to its rightful size. Any discussion on what a fair tax rate per person is is irrelevant UNTIL we control the spending.
I don't know how much the poorest pay right now, so I don't know if they are paying "Too little" or not. My view is that ultimately, everyone benefits from the (Properly limited, there are certainly people, such as drug users who are incarcerated, who would be better off without any government than with the current American government). I also haven't calculated what the government programs I actually want (Pretty much only defense at the Federal level, and also police, courts, roads, and education at the state or local level) would cost, so I don't know how high taxes would need to be to pay for that. So my position isn't so much "The tax rate needs to be X" as it is "Spending needs to be limited to Y, with taxes as necessary to pay for it".
The truly fairest way to go from here is to tax everyone in accordance with how much they benefit. To the extreme this means user fees on everything, but that's not really possible because of externalities and all that. The next best thing is to try and guess.
I think it would still be pretty tough to guess accurately, so I don't insist on this. Certainly the rich benefit more from even what I would consider a just government than the poor (Having their property rights protected is much more important to them than the poor) and so they should certainly pay a higher dollar amount than the poor (I've never heard of anyone arguing for everyone paying exactly the same dollar amount, except rhetorically to prove the "Same percentage" argument wrong, but I figured I'd distance myself from it anyway.) Of course, with the flat tax, they still do pay more, much more, than the poor.
While I do think the fact that government protects the property rights of the rich should be taken into account when it comes to taxing the rich, this should only be the case up to the extent that it does in fact cost money (And it certainly does cost some) to protect their property. I don't think you can say "We can take as much as we want because we recognize your right and you benefit from that" while still being moral for a few reasons.
Firstly, it isn't strictly true that the rich can protect their property only through government. Government makes it easier, but it does not make it possible. People could voluntarily recognize property rights due to contracts made. Businesses could hire their own security/bodyguards, heck, even court systems, if there was no government. That would, at least possibly, lead to a nightmare scenario where wealth IS the law, rather than the law simply not protecting wealth. I don't see this as desirable, so I disagree with the anarcho-capitalists, even while admiring a lot of what they say.
Secondly, even if it were IMPOSSIBLE to protect property without government, government still has a duty to protect it because its a human right**. Now, as stated, the person who wants them to protect their property still owes them the cost of doing so, they shouldn't get to redistribute those costs to someone else, but if a state is going to claim a monopoly of force (Or close to it, my vision of a "State" does not have the same degree of "Monopoly of force" as a typical state, although they are still the main users of defensive force in my vision) they have a duty, in my opinion, to protect property at no profit to themselves (I'm not counting the costs of doing so, or the salaries of the people who do so, as "Profits"). They cannot "Compete" by charging higher prices, because they have a legally protected monopoly.
Ultimately, I think a straight up tax on property seems like the best solution, since that's the main service the government supplies. Own a lot of property, pay a lot of tax. Own a little, use a little tax. Roads could fairly easily be paid for by user fees, its called tolls (Which also discourage pointless use and so helps the environment, for all of you "Green" folks

). I'm no expert on taxes though, so I'm in no way certain of this. I'm much more concerned with the amount of spending and taxes than I am with the exact modus operandi of collection.