Flat taxes aren't entirely detrimental for poor people, they are only severely advantageous to the rich. Proposing a flat tax as the "savior to the poor" is just wrong.
If you make $2mm a year, single, no home, no wife and kids. Currently, you should owe about $745k in taxes. A flat tax drops that to $300k. A flat tax just made this person $445k extra.
Since public services aren't getting cheaper anytime soon and governments aren't really role models in modest spending... where do we come up with this gap? Now if the rich person could donate his extra earnings to a charity of his choice that would be great but who really is that benevolent? Plus, that's just the start of more special interest groups.