It means stripping away unnecessary rates and unnecessary levels of taxation. It means moving the point of collection as close to the source as possible. And it means moving any necessary complexity away from individuals and toward businesses, which are better equipped to deal with it. The flat tax achieves all of these goals. Thus it would significantly simplify the tax system.
All taxes impose a cost on the economy over and above the amount of actual revenue collected.
Economists call this the excess burden or deadweight cost of the tax system. It is in addition to the compliance cost. Although all taxes impose some deadweight cost, the magnitude of the cost varies enormously depending on how the tax system is structured. Two different tax systems raising the same amount of revenue can impose significantly different burdens on the economy. At the low end is the head tax or poll tax.