[weaksauce]

There are two definitions of a regressive tax. the first deals strictly with the percentage rate and the second deals with the proportionality of effect toward lower class incomes. Your flat tax would be strictly progressive on the first front but regressive on the second even more regressive if tax deductions are still a thing. The only fair tax is one that is progressive and accounts for diminishing marginal utility of a dollar. Just like sales tax is a flat tax it's regressive because of the elasticity of demand for essentials.