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.
Friedman proposed a negative income tax in Chapter XII of Capitalism & Freedom, published in 1962. In that chapter, however, he does not tie the NIT to a flat tax but allows that the subsidy (negative tax) rate could be “graduated just as the tax rates above the exemption are.”