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.”
I’d have to check, but in his Free To Choose documentary, I believe you will find that he changed from the NIT to a flat tax, and a big part of that was because he believed it would remove some of the politics from setting taxes.