Actually, Milton Friedman favored a negative income tax so his preferred tax function was linear with a negative vertical intercept. This, of course, makes the tax system “progressive” (the average tax rate rises with income) but much simpler than “progressive” tax system with nonlinear tax functions.
Most flat (income) tax systems I have read about over the years eliminate the corporate income tax altogether. In those schemes, income taxes are levied on individuals only, and that includes “business” income distributed in the form of salaries, capital gains, profits, bonuses, or dividends - all taxed at the same (flat) rate. Retained business income is not taxed until it is distributed to an individual.
Actually, I was lucky enough to have dinner on two occasions with Friedman. His original position was a flat tax passing through the origin. When he started advising Reagan, Reagan told him that, politically, that would never fly, which is when he conceded to the negative intercept. It also allowed Reagan to say that he was still keeping the progressive tax structure.