No. Someone making $20K a year shouldn't have to pay the same percent as someone making $500K.
If there was a society where wealth disparity was reduced, say, so the richest make only 4x as much as the poorest, I'd be fine with a flat tax.
Depending on whether the flat tax has a minimum threshold or not they may pay less. If no minimum threshold than they pay the same, but if a minimum threshold, their marginal rate will be the same but effective rate will be lower. Say if 10K is tax free and the flat tax is 20%, then someone making 20K would only pay 10% while a person making 500K would pay 19.6%