Eliminate the IRS. Establish a Consumption Tax.

We need a tax system where everybody participates/contributes to the system. By hiding income, one can still cheat the flat tax system. The consumption tax is fairly dispersed across the board.
The consumption tax is a perfect example of a free-market system. It is a voluntary tax. If you don not wish to pay the tax, do not purchase the item or service.
It would also take care of nonprofit tax-free organizations. No one would be tax-free because everyone and every organization must purchase things.