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The standard data shows that the tax system is overall progressive. This chart combines CBO estimates for federal taxes with ITEP estimates for state & local taxes. Federal income taxes highly progressive, when you add in payroll/state/local/etc. is still progressive but less so. 
It is not clear why you should just look at the tax system without looking at what it funds. eg, is Social Security a regressive 12.4% tax or a progressive overall system that reduces poverty and inequality? This chart shows the combination of taxes and means-tested transfers.
Lots of caveats on the previous. I did non-elderly to avoid issues around seniors looking temporarily lower-income than on a lifetime basis. And also excluded Social Security and Medicare. Arguably should count all those in which case even more progressive.
Also this just values government transfers and values them at cost. Arguably spending on courts and national defense does more for Jeff Bezos than it does for anyone else named Jeff in the entire country because it helps to support and defend his wealth.
And all of these estimates, tax and spending, depend on a lot of assumptions. These are the assumptions from CBO, which I've generally found to be reasonable--albeit imperfect and hopefully improving over time.
This matters because the way European countries achieve greater progressivity than the United States is not primarily on the tax side but instead in the benefits they provide--like for education, pensions, healthcare, and unemployment. Ignoring those risks missing the plot.
