Proponents of a flat tax system usually suggest a large personal allowance to go with it to take the poorest out of tax all together.
Exactly. You have something like 16,000 per year tax allow for a single person (or whatever value makes sense to pay for rent, utilities, food and basics), this can increase in more expensive areas and increase with children, of you care for an elderly or sick relative etc, etc.
This threshold is basically what constitutes are reasonable living standard.
A flat rate tax is actually much better for the poor, they can end up pay much less tax. Then you have a flat rat tax on the rest of the income above the threshold.
The more you earn above the threshold the more tax you pay in a linear and fair way. If you earn twice the amount above the living threshold you pay twice the tax, can't get fairer than that. The more disposable income you have the more VAT taxed items you buy and the lower your cost are to society, e.g. with private health care, and the more you contribute employment by hiring cleaning/gernening/DIY people.