Rick Perry's "flat tax"

It isn't flat.

Perry says he's against progressive taxation and wants a tax code "that you can put on a postcard." But his own plan doesn't eliminate the federal income tax rates. He keeps those rates but adds an alternative flat tax, which you're apparently free to choose or reject. So he seems to want to complicate the federal income tax. You might still be able to write his plan on a postcard, by writing out the 6 tax brackets plus an alternative flat tax. On the other hand, that means the progressive tax could also fit on a postcard.

There's no significant difference between Perry's plan and the current income tax as far as simplicity or length. The real difference is that, as the first link explains, Perry's plan would be a huge tax cut for the rich, which would decrease revenue, which would increase the deficit.

Perry says that reducing tax revenue would be a good thing, since then we'll need to reduce federal spending. "All of these tax cuts will be meaningless if we do not control federal spending." So he seems to subscribe to the "starve the beast" theory. Well, that theory has been tried, and it doesn't work.