That is an interesting video but I think it is engaging in a lot of sleight of hand. Let me go over some examples of what I mean -

1. If you take the video at its word, then it is still the case that the richest are paying more taxes. In the final graph the richest decile is paying over 30% while the poorest is in the mid 20's. The curve is slightly crescent shaped, with the poor 20-30% paying less than the poorest, but beyond that the trend holds that richer pay more. The video summarizes this slope as "mostly flat".

2. The video adds 15% for payroll taxes to the poorer deciles even though the video says that 7.5% is paid by the employee and 7.5% is paid by the company. The video explains that "economists have found that in practice companies pay their part of the payroll tax by just paying workers less." The video doesn't offer any source for this claim. If you Google the claim you see it is, not surprisingly, disputed by economists. It's not a plausible claim in the first place, and if you are allowed to support a claim because some economist somewhere might have said something kind of like it then you could really claim anything. Once you adjust the 15% the video incorrectly added to every lower decile back to 7.5% then the trend of the rich paying more, which was always present, becomes even more prominent.

3. The chart shows the richest 400 Americans as a column on par with the other deciles. This is visually deceptive because it causes you to think of this category as being a similar kind of thing - but it is not, it's a much smaller and extreme group. These people made massive amounts of money from stock in huge companies, gains which are often unrealized, and so taking this small group and graphing it next to deciles distorts what is being shown. How would the graph look if we added on the 400 poorest Americans? And why would we do that except as some rhetorical trick?

4. The video is uninterested in net taxation. That is, poor Americans get significant transfers of money back from the government. For some groups this is substantially more than they pay in taxes which would make their net interaction with government profitable. I can't really agree that a group "pays" X% in taxes if they receive from government transfers more than they paid.

5. The video description says that "All of their data, which we used to produce this video, is available on their website." But it's not. At least, I hope it's not all the data they used to produce this video. There are a few unexplained Excel sheets with some unsourced and unexplained data on the "Tax for Justice" website, but nothing like what I would expect to underlie the claims made in these figures. For example, I wanted to look at how they calculated the sales tax rates, since those varied by state and I thought that the poorest people might be spending more in categories that have no sales taxes (e.g. food) - but... maybe I didn't look hard enough, but I couldn't find anything like this. Just some random tables with numbers.

6. The top decile earns about half the income for the country. They also pay the highest tax rate. So, it's pretty obvious that, in objective terms, most of the taxes are paid by the rich. Even if, pre-benefits, the poor paid tax rates that were only ~10% lower than the richest decile, the richest decile would still be paying substantially more objective dollars in taxes.

7. It's also a bit weird to me that Vox, nominally a news organization, would just uncritically repeat the work of left wing activists out of Berkeley. Is regurgitating advocacy what a news organization is supposed to do?