I think all income, regardless of source, should be taxed at a flat rate. It's how it works for tithing in a lot of churches, and it's a very simple but effective system.
As Buffett points out, they don't. Buffett's is lower, because capital gains are privileged with a substantially lower rate, because the mega-wealthy largely benefit there.
If you optimize for simplicity, but at some greater cost to having a society that functions for all its citizens and residents, is it worth focusing on simplicity?
The higher you go in income, the greater the proportion goes to things like retirement, investments, entertainment, etc. Millionaires (i.e., earning > $1M/year) paying 15% don't worry about eating well or enough, or being cold at night or losing their job because their car breaks down, or even whether they can pay for college for their kids.
This is why flat taxes are regressive, and if you propose a bottom line exemption (e.g., < $20k/year pays no tax, or less tax), it's not a flat tax anymore, it's a progressive tax, and we're just haggling over the details.
If Buffett's secretary pays $20k in taxes, and Buffett pays $21k, is that fair because he's still paying more?
How much lower can his tax rate go versus his secretary's rate before it's unacceptable?