They become billionaires not by receiving income directly, but by holding assets that appreciate in value. A progressive income tax isn't going to do it. We will need some variety of wealth tax. The major criticism against a wealth tax is that their wealth is in stocks, and a tax would require them to liquidate their shares in order to pay the tax. That would crash the market.
Which is why we should just tax the shares directly. Take the shares. Send them to an IRS liquidator, who can sell them off slowly, such that liquidated shares never comprise more than 1% of total traded shares. The sale of those shares won't have a significant effect on market value.
It might take years or decades to liquidate what they collect, but over time, such a tax will drive stock ownership away from the ultra rich and toward the working class.
My mistake. Have a nice day.