Your first sentence is true, but a flat tax entails a sales tax, sometimes given the slightly different-in-meaning euphemism “value-added tax,” which hurts low-income people more than high-income people, so many black people would be very foolish to be in favor of a flat tax.
A flat tax is NOT in any way a sales tax any more than any other income tax is a sales tax. Sales taxes at a national level are every bit as bad as the progressive income tax.