I think your "flat tax" is not "fair". Why should taxes be tied to income? I think a more "fair" way is for everyone to pay the same AMOUNT of taxes.
That would also be much simpler. Let's say the annual cost of government is $X.00. Divide that by the number of citizens and we each get the same bill. What could be more fair?
You can define "citizen" any way you want. We all benefit from the government, so we should all pay the same amount for "government services". Why should the cost of government be any more or less than the cost of a mechanic's services, a lawn maintenance service, or any other service? Here's what it costs. Here's your bill.