I'm fairly new to PD myself (been a user for about 2 days), but give this a try:
1) in the upper right of a report or chart, click the "edit chart" option
2) To the right, click on the 2nd icon "Chart Format" scroll down and expand " > Advanced"
3) Under CSV, check the box for "Expose Public CSV URL" then copy and paste that URL in an open browser tab.
It would appear that the intent of this feature would be to expose a direct downloadable path to the underlying data in a chart.
When I tried this myself, I encountered the following message:
"Chart does not have api access enabled - chart must be saved after enabling api access"
This message would point me in the direction of an admin to enable API access, then update the chart.
There are likely other ways to do what you're asking for, but after doing some picking around the UI, this was the first thing I came across. Again, I'm a very new user, but this path makes sense to me.
Please let me know if how this shakes out for you. I might have similar questions in my org later.