The link that he gave already adjusts the numbers for payroll taxes (but it's obvious from looking at how the tax is collected that it's regressive -- i.e., flat rate up to $106k and then no tax on wages above that).
The link he gives does not provide % of tax burden / % of income earned, nor do I see any way to figure that out from the data given.
I agree that payroll taxes are regressive past $106k, but it's hardly clear that this changes the picture significantly. I.e., the 12.4% a poor person pays in payroll taxes need not outweigh the 0% they pay in income taxes.
Second, the use of the federal itemized deduction offset is very misleading, given that the deduction's purpose is to avoid double taxation in the first place, and that the money states get from the federal government comes almost exclusively from progressive sources.
Third, the intersection of the previous two. Most of the difference between brackets regardless of states is accounted for by the wealthy paying very little sales tax. They pay very little sales tax because they consume very little of their income. What they don't consume ends up being taxed in the estate tax mentioned earlier or given to charity neither of which are included in this report but both of which pay for similar things to state taxes (helping the poor, schools, libraries, parks, etc)
With regard to state taxes, this report gives a pretty thorough analysis for all 50 states: http://www.itepnet.org/state_reports/whopays.php
It's pretty evident from the data in this report that state taxes are very regressive in most states, mostly due to sales taxes.