Treating all earnings the same is a separate issue which has absolutely nothing to do with whether a given tax is flat.
Not really. All "earnings" are "income". Different rules for income from different sources means a non flat income tax by definition. What you want, apparently, is "a flat tax rate on certain income, retaining the existing exemptions that are beneficial almost exclusively to high income groups" Which is a defensible position, but not in any way related to a "flat tax".