Since Flash has its own data management tool, I doubt any browser would be able to enable shortcuts to clear this data.
Are you saying that the "Adobe Flash Player Storage Settings" on this page is what controls caching of files?
Just hover over the search result, then hover over the arrows that appear to the right of the result.
On a Mac, it's Shift Command R, or holding down Shift while clicking the reload button (as opposed to Command R or a normal click for a regular refresh).
So when you visit the same page for a second time, the browser speeds up display time by loading the page locally from cache instead of downloading everything again.
Although storing Internet cache makes web browser faster as it usually takes your computer less time to display a web page when it can open page's elements or even the entire page from your local Temporary Internet Files folder, You sometimes want to overrule the Internet cache, for Example to see changes you made to a webpage you just uploaded.
[Existing bug log on this issue] Closed as a duplicate, the issue remmains: [Issue: 94090] .
I think this is either the date I uploaded my old Gravatar, or the date I signed up for Gravatar.