Sorry, not buying,
With a flat tax you do pay more the more you earn.
Progressive taxation though is an abomination. Right up there with the politics of envy.
I can go with flat tax so long as it starts near median wage levels. Assuming family median wage is around $60k/year, first $48k (80% of current median income) EARNED income should be tax exempt and then apply flat tax for all income above that level.
We want incentive for low wage earners to keep working instead of collecting welfare.