Not fairness
You also make the contradictory claim that fairness should have nothing to with the law and then turn around and justify a flat tax using a synonym for fairness.
I'm not saying a flat tax should be imposed because it's fair, although in my opinion it would be, but because it is equitable. The law should treat everyone the same. The purpose of the tax code isn't to make one group pay and to reward another group; it's to raise revenue for government expenditures. That should be it's only purpose.
As for the judicial system being skewed towards the wealthy, you're right. Our system's broken in several areas, but that doesn't mean we should break it everywhere.