A few points, but I am not sure which one you are referring to:
- interesting enough actual taxation in the US seems to be mostly flat in practice (after a certain threshold): rich people get more deductions and can hire lawyers to use all the loopholes
- you can have a mostly fixed marginal rate of taxation on income, but still have progression in average rates. Eg give everyone $10k/year as an allowance, and tax at a fixed 20%.
- for taxes on income there's a trade-off between equality, ability to pay, but also blunting incentives and raising revenue. Luckily, if you tax land value instead, you can tax away essentially the whole of land rent without blunting any incentives to work or invest. (So the whole conundrum about the right way to tax income can be mostly side-stepped.)
I'm about to move to Singapore. They have a progressive income tax system with almost no deductions, but the maximum marginal rate is 22%. (VAT is 7%.) Since there system is so simple and rates are low, it's usually easier to just pay instead of trying to find loopholes.
Even in your follow up post as soon as we make provisions for the reality we live in the flat tax goes back to being a progressive tax, again.
So what we really need is a simpler progressive tax rather than a gradually complex flat tax.
Singapore and Hong Kong seem to do the right thing in terms of taxation: their systems are simple and the income tax is progressive, but the top marginal rates are pretty low by European standards (around 20%).
To help the poor, universal basic income seems like a good idea. It pairs well with my favourite kind of taxation: land value tax. See https://medium.com/basic-income/why-land-value-tax-and-unive... for a pretty insightful rant.
If an income tax is necessary at all, giving everybody a flat allowance per head plus a pretty flat rate should be good enough on the poor? (Otherwise, do whatever Singapore or Hong Kong or Estonia are doing.)