The problem is this sort of a tax scheme would drive the national debt through the roof at an accelerated pace. The amount of revenue lost by giving the rich the biggest tax cut in history would create budgetary red ink with no end.
The wealthy would not pay more with a flat tax. A flat tax would be a tax cut for the wealthy. With all the loopholes they now enjoy they still pay about 18% to 20% of their gross income in taxes. You are proposing eliminating the loopholes with a 10% flat tax and therefore cutting their taxes in half.
Hey! Here is an idea, instead of dealing with the increasing debt by taking more money from tax payers wealthy or otherwise, let's just stop the spending.