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I sincerely doubt that any of the founders would have approved a progressive income tax, or any income tax at all. In fact, according to their final work product, the Constitution and the Bill of Rights, they expressly did not. They did, however, allow for an excise tax.

Interestingly, it was considered and even implemented prior to being resurrected in its current form. I don't know how they justified it prior to the Constitutional Amendment.

The first income tax suggested in the United States was during the War of 1812. The tax was based on the British Tax Act of 1798 and applied progressive rates to income. The rates were .08% on income above £60 and 10 percent on income above £200. The tax was developed in 1814 but was never imposed because the treaty of Ghent was signed in 1815 ending hostilities and the need for additional revenue.
The Tax Act of 1861 proposed that "there shall be levied, collected, and paid, upon annual income of every person residing in the U.S. whether derived from any kind of property, or from any professional trade, employment, or vocation carried on in the United States or elsewhere, or from any source whatever.
The 1861 Tax Act was passed but never put in force. Rates under the Act were 3% on income above $800 and 5% on income of individuals living outside the U.S.
The Tax Act of 1862 was passed and signed by President Lincoln July 1 1862. The rates were 3% on income above $600 and 5% on income above $10,000. The rent or rental value of your home could be deducted from income in determining the tax liability. The Commissioner of Revenue stated "The people of this country have accepted it with cheerfulness, to meet a temporary exigency, and it has excited no serious complaint in its administration." This acceptance was primarily due to the need for revenue to finance the Civil War.
Although the people cheerfully accepted the tax, compliance was not high. Figures released after the Civil War indicated that 276,661 people actually filed tax returns in 1870 (the year of the highest returns filed) when the country's population was approximately 38 million.
The Tax Act of 1864 was passed to raise additional revenue to support the Civil War.
Senator Garret Davis, in discussing the guiding principle of taxation, stated "a recognition of the idea that taxes shall be paid according to the abilities of a person to pay."
Taxes rates for the Tax Act of 1864 were 5% for income between $600 and $5000; 7.5% for income between $5001 and $10,000; 10% on income above $10,000. The deduction for rent or rental value was limited to $200. A deduction for repairs was allowed.
With the end of the Civil War the public's accepted cheerfulness with regard to taxation waned. The Tax Act of 1864 was modified after the war. The rates were changed to a flat 5 percent with the exemption amount raised to $1,000. Several attempts to make the tax permanent were tried but by 1869 " no businessman could pass the day without suffering from those burdens" The Times. From 1870 to 1872 the rate was a flat 2.5 percent and the exemption amount was raised to $2,000.
The tax was repealed in 1872 and in its place was installed significant tariff restrictions that served as the major revenue source for the United States until 1913.

source

Jefferson in particular seems to favor "progressive" taxation:

"Taxes should be proportioned to what may be annually spared by the individual."
--Thomas Jefferson to James Madison, 1784. FE 4:15, Papers 7:557
"Another means of silently lessening the inequality of property is to exempt all from taxation below a certain point, and to tax the higher portions of property in geometrical progression as they rise."
--Thomas Jefferson to James Madison, 1785. ME 19:18, Papers 8:682

If the income tax were to continue, I myself would favor a "flat" tax, with personal and dependent deductions only to alleviate the burden on those on the lowest rung of the economic ladder.