A flat tax is inherently regressive. A highly progressive tax rate, as the US had from the 30s until Reagan scrapped it in the 80s, brought exactly the broad middle class that brings stability and continued growth to the nation as a whole.
Tax enough to keep the number of obscenely wealthy extremely small, and still not orders of magnitude wealthier than the middle class. As it used to be.
Tax capital like income (also as it used to be).
Do not allow stock buy backs (also as it used to be).
There are lots of other things to be done, but those alone would improve the US economy massively.
We know this is true because we've already done it.