Since a flat tax is inherently unfair, the only fair percentage would be zero percent.
A flat tax is a regressive tax, which means it harms the poor more than the rich, proportionally. This is largely because the poor spend a greater portion of their total income than the rich.
The rich save a greater proportion of their income than the poor. Not just in total dollars, but in proportion, as a percentage of their total income.
In addition the poor spend a greater percentage of their income on essentials like clothing, food and rent.