I guess the authors of the constitution shouldn't have bothered to enumerate any powers of government, since in your interpretation "general welfare" contains any conceivable power whereby congress could argue that it promotes "general welfare". Locking everyone in their homes could be argued as "general welfare".
If the flat rate were, say, 7%, someone making $10K/yr would pay $700/year. Someone making $1M/yr would pay $70K/year. So, unless you're mathematically challenged, surely you can see that $700 =/= $70K.
Given that this is just an exercise, we don't need to define every detail of the plan. But if you insist, military spending is clearly within an enumerated power. So national defense, per se, would be included in the flat rate mandatory tax and would be subject to congressional over-site as it is now. Social security would obviously be impacted. Since the government doesn't have the authority to redistribute wealth, such a government program would be completely voluntary. <gasp/>
But to your question, I don't think every line item detail needs to be a check box. Congress would define what the check boxes mean. You check the "social security" box, it means whatever the law says it means. But do keep in mind, this is just an exercise to get people to think about the ways we use government to control the property of other people, especially when our own property isn't even in the game.
If I'm not paying taxes, what right do I have to tell other people what they should pay? What right do I have to vote their money into my bank account? How is it moral for me to say that people who make more than me, and are actually paying a higher portion of the nation's tax revenues than me, aren't paying their fair share? We try to say the 1%'ers are immoral for not paying even higher amounts, yet neither of us even earns in a year what these people pay in a year in taxes.
The secretary who complains that she pays more taxes than her CEO is not making an honest argument. She may pay a higher percentage of her income in taxes, but to say that means she pays higher taxes is an outright lie. Mitt Romney made somewhere near $20M in a year, and paid like $3 million in taxes. That secretary won't even make in her lifetime what Mitt Romney pays in taxes in one year. It's dishonest to say she pays more tax than he, and it's immoral to say he doesn't pay his "fair share".
Perhaps it is information like THIS Where Mitt Romney Hides His Money - Business Insider that might move some to think Mitt isn't intent on paying his 'fair' share
My problem with a 'flat tax' has always been that the people who flatten the tax can also open loopholes. I forsee '17% flat tax' and the removal of all deductions for the little people, followed by gradual opening of loopholes in the tax code, followed by a further increase in the tax rate for the 'proles' because "... revenues do not meet projections" - and all tax relief/deductioins for ordinary people are gone forever because they lack the resources/influence to buy enough congresspersons to even get a seat at the table