So you want to argue about the constitutionality of any/all non-flat taxes?
It is, I believe, the 16th amendment which states, "The Congress shall have power to lay and collect taxes on incomes,
from whatever source derived, without apportionment among the several
States, and without regard to any census or enumeration."
Although the 16th didn't come into being until later, the first income tax was levied in 1861. At first, Congress placed a flat 3-percent tax on all incomes over $800 and later modified this principal to include a graduated tax. Congress repealed the income tax in 1872, but the concept did not disappear.
In 1894, as part of a high tariff bill, Congress enacted a 2-percent tax on income over $4,000. The tax was almost immediately struck down by a five-to-four decision of the Supreme Court, even though the Court has upheld the constitutionality of the Civil War Tax as recently as 1881.
In 1909 progressives in Congress again attached a provision for an income tax to a tariff bill. Conservative, hoping to kill the idea for good, proposed a constitutional amendment enacting such a tax; they believed an amendment would never receive ratification by three-fourths of the states. Much to their surprise, the amendment was ratified by one state legislature after another, and on February 25, 1913, with the certification by Secretary of State Philander C. Knox, the 16th amendment took effect. Yet in 1913, due to generous exemptions and deductions, less than 1 percent of the population paid income taxes at a rate of only 1% of net income.
If you want to read all about the 16th amendment and related court cases I would refer you to
http://www.access.gpo.gov/congress/senate/constitution/amdt16.html