Only if you ignore sales tax, car tax, property taxes, and other such taxes.
The top 10% typically included major corporations but without a source I don't know if the percentage you use does.
Saying that I'd be all for a Federal sales tax of 20% if we could nearly eliminate income taxes.
Contrary to popular belief, the so called utopias like Sweden, tax the poor at almost comparable rates as the rich.
The poor already spend all their money on necessities. If you go to a flat sales tax it will hurt them more than the current progressive regime and favor the wealthy.