Russia tried a 13% flat tax. And for the most part it accomplished what it set out to do; get tax evasion and the black market economy under control. Those problems are not anywhere to the severity here in the US that was seen 1990's and early 2000's Russia.
To fund the social programs, infrastructure, and military that people want, the tax is going to need to be quite high in the US. 13% won't cut it. The number is around 35% flat tax to hang onto what we have today without borrowing. And that does not answer what we do with people where a 35% haircut to their income means they are short on rent.
We are a nation that can put men on the moon, build the largest nuclear-powered naval fleet in the world, and collect and tally the votes of over 150 million registered voters. I think we can figure out how to count your income, subtract each bracket off the effective earned income, and tally up the rows to get you a final tax value. If you want to know your effective rate, take that value and divide it by your gross income.
That said, if we really don't want to do arithmetic anymore, then perhaps we could save a little money by ending our math education. Imagine the tax savings if we lower our standards and create a generation of ignoramuses.