Isn't a flat tax just that? With a flat tax, there are no deductions or tax credits so your Husband's wages at 13/hr would be taxed at 5% with no tax credits, no "getting more back in taxes".
By the way, this flat tax would in no way be 5%, it would have to be more than that, I remember seeing 17% floated. In which case, your husbands 40 hr wk at $13/hr would be taxed at 17%, or a tax bill of $88 per week. Your $560 paycheck goes to $472 of course then you are levied for social security and state income, leaving you with around $400/week. Your mortgage is what, around $660, so you'd have about $1000 to pay for everything else -- lights, heating, gas, car repair, clothes, medical expenses, food and so forth. I'm glad you can do it but that's not leaving you with much margin for savings in case something unexpected happens, like your husband getting hurt.
The income tax was always intended to be a progressive tax. Those that make more can afford to pay more. Its better for you and everybody else if you have a little more for taking care of your own.