I'm in favor of a gross revenue tax with no loopholes. Take all the money that came in, apply and percentage and pay that. No special tax rates. No expenses. Nothing outside of a percentage that to me should be progressive but would be a lot lower percentage than today because of no loopholes or expenses.
I prefer progressive also.
Flat tax gets tricky unless you have high minimum wages. Basic foodstuffs cost money, and poor people need to eat.
The advantage of reducing loopholes, or otherwise simplifying the system is in reduced cost of administering the system, also.