I have proposed a similar plan in the Loft. My main issue with yours is that it creates a large marriage penalty.
For example, if the flat rate is 25%, and Joe and Jane each make $25,000, then their combined tax bill is $0. But if they get married, their tax bill becomes $6,250; the system just punished them by $6,250 every year for the act of creating a more stable household, which is a socially desirable act that we want them to engage in. That's a problematic incentive structure.
To get around that, I allowed for $20K for each adult, tax free, and an additional $5K per child, in order to keep the zero-tax point at about 200% of the poverty line. I'd welcome any critiques or comments.