Flat taxes address the wrong problem. It's easy enough for individuals and corporations to look up their tax in a table once gross income (or profit) is determined. The complication is determining what counts as income, and flat tax schemes don't do anything to address that complication, particularly for corporations.

Most corporate tax avoidance strategies take advantage of laws intended to prevent different countries from taxing the same dollar of profit, and those rules will still exist in any reasonable tax structure.