The actual report is here.

During the time periods described, were conservatives running things the whole time? Or even most of the time?

Did you notice that while you're supposed to compare Figure 1 and Figure 3, that Figure 1 covers 25 countries, while Figure 3 covers 8 carefully selected one. Where are countries like Japan in Figure 3? Anybody notice the abundance of "bedroom nations?"

Did you notice the quick switch of vertical scales on page 8 in Figure 9 to artificially dramatize something that the top graph shows to be a relatively steady trend since the early 70s?

There are other little tricks, like the "fine print" in the footnotes.

Income for Figures 4 and 5 is adjusted using the Consumer Price Index Research Series Using Current Methods (CPI-U-RS). Personal income and family income include before-tax earnings, interest and dividends from capital, cash benefits from government programs (such as Social Security, welfare, or unemployment compensation), pension or retirement income, child support and other cash income. It does not include the value of non-cash compensation such as employer-contributions to health insurance and retirement benefits, nor do they include the effect of taxes or non-cash benefits such as food stamps.

I wonder what the graphs would look like if you threw the tax burden into it?

Are you aware that the payroll tax rate in 1964 was less than half of what it is now? You remember payroll taxes. The ones even the poor workers pay. In the 1950s it was less than a third.

Meanwhile, the U.S. Federal government has almost quadrupled in budget since 1964, in constant dollars. Hey, wait, look at that CEO over there!

The entire "rate of growth" thing is suspicious. Of COURSE the rate of growth from one generation to the next is going to slow as overall wealth increases. Did you think the slope that we had in the 1800s was going to go on forever?