While pre-Reagan the game was in the thousands of "loopholes", the bigger game now is the definition of "earn" or "income" itself as
@wllm1313 has explained a few times. A zero deduction, a zero "loophole", zero off-shore tax haven, flat tax would still result in millionaires paying zero taxes because the flat tax is against INCOME, not unrealized asset gains. 10% X zero is still zero.
We have to find a way to have this huge source of wealth (and dare I say income) subject to the same taxes 95% of Americans pay through payroll income taxes, without creating a system with unintended consequences/incentives that destroy the underlying asset value (think of passing down the family farm to the kids - if the tax consequences are too steep, selling it off is the only option).