Since the rich don't pay taxes, and the poor (unemployed) get only money from the state, there is no redistribution from the rich to the poor. There is redistribution from the middle class to the poor, right?
I seem to recall some graph indicating that even though they pay 4-5x (or higher) lower percentage of their money in taxes, the higher amounts mean they shoulder most of the tax burdon.
I don't think the percentage difference is ultimately beneficial to society, but it's not correct to say they pay nothing.
http://www.pewresearch.org/fact-tank/2016/04/13/high-income-...
And then here, merely the top 10% of wealth holders hold 76% of the wealth, and the top 20% of wealth holders hold 85% of total wealth. The statistics are no where near what you appear to be claiming.
https://en.wikipedia.org/wiki/Wealth_inequality_in_the_Unite...
Anyway, I never looked very deeply into it, but I'm pretty sure that single-digit millionaires pay plenty of taxes, and I find it fair to call them "rich." I do agree that taxing income much more heavily than capital gains, property, etc. doesn't sound like a great idea.