Any "flat tax" is a regressive tax. That includes property tax, sales tax, the taxes (called fees) we pay for drivers licenses and car registrations, etc. As I have said before, we should get rid of all of that and replace it with progressive state income tax. Then all taxes are based on one's ability to pay, with the wealthy paying more, as it should be.
You could address some of the issues with capital flight that way, an income earned where someone is working, where there job is, could be targeted in that way but in the UK when this has happened the boardrooms and higher salaried positions have just renegotiated their contracts in order that instead of income they get shares or other types of payment which are not taxed.
The only conceiveable argument for lower taxes on the higher incomes for me would be that at a certain point the costs of avoidance and evasion outweigh the cost of compliance with collection, public revenues do reflect that, it is a fact, and it could go some way to practically raising the necessary money for public expenditure, which in the UK at least had become a serious, serious problem (and probably wont be sorted out for a few generations).
This was not that public expenditure was unaffordable, the "great resignation", "lone parent families", "welfare dependency", or any of the other classic conservative bogeymen were not to blame, or any of the nouveau anxieties about "breeders", "over population" etc. (many of which are just trojans for older folk devilry anyway, "the poor they are too many" or racist thinking, in drag, to appeal to the sensibilities of new money homosexuals a lot of the time).
The existing and projected spending could be covered that way, even better spending on public services or infrastructure could be covered that way, depending on political choices, it could as easily be used to pay for tax relief for the mega rich as it was with Trump's administration, with no evidence what-so-ever of it resulting in anything other than nominal changes in private accounts of already obscenely wealthy individuals as they play games of who will be the richest man in the cemetary.
The problem is wealth inequality, specifically, I think, old money, and there is a problem in so far as it appears to be invincible and impervious to any type of taxation, market correction or control what-so-ever. There is no recession, depression or political decision making which will actually touch a certain population of wealthy elites, I'm increasingly no convinced that this group is effected by war, disease, racism or other prejudices, even law, moral or normative sanction can not and does not impact upon them, its not like anything that's been known in the past and you maybe only get a glimpse of it within some fictional narratives, for instance Dune.
A lot of the "minor controversaries", like those I mentioned already, but also environmental catastrophizing, climate change etc. and even the resistable rise of the various fascisms, biological vandalism and new chauvinisms, which begin trending, are just attempts at reforging connections, like the lilliputians attempting to bind Gullivar.
I largely suspect that the same elites will carry on ignoring the major social and environmental externalities, the wealth inequality will continue apace, all the older ideologies dont even have a proper way of conceiving what is happening or suggesting any alternative which does not amount to the "same old, same old", they are all really spent and exhausted, whatever the appeal of old fashioned racist ideologies have at the moment, I think its a flash in the pan, the final arbitor is money power, money values and old money trumps that.
A hell of a lot of forums online are dominated by discussions which are just trojans one way or another for this kind of thing, even the honest standard bearers opposing it dont realize the extent to which they've been wound up and set off in a fashion to provoke or amplify enmities which result in eventual spikes in what they are enthusiastically "resisting". The real world is changing to conform to that style too. Silencing or censoring or otherwise policing opinion, as it often is online and always through formal sanction, doesnt make it go away, no more than battling with private doubts or internalised voices on the same topics within the self means it goes away either. Though I do, ultimately, think its a side show, it all seems to me like children at a party squabbling over whether their favourite type of ice cream should be the only type of ice cream.
Whether or not the world can or should conform to your own thoughts, feelings, preferences is the stuff of politics and public discourse, not wealth inequality, even paying for public spending reflects the former rather than the later and always will. Which kind of makes much of it all a mute point really.
And that mute point nature is why I think there's declining interest in some forums, types of discussion, discourse or public engagement among people who arent part of the elites. Meaning the types of opinion that come to dominate are the most garish, nonsensical types, the idiocracy types, and you then have echo chambers the world over. Its what I've observed here over the last couple of years as an on looker.