Since we've been getting quite a few threads about this topic, and there likely will be more in the future yet, we've decided we'd make this PSA/heads up to hopefully answer all questions before they crop up.
TL;DR: Nothing will change on e621 itself, we will not be deleting any files, nor will we prevent the upload of new files. However in order to view flash files in the future you will likely need to download a standalone flash player projector and play the games/videos locally.
Long Answer: The death of flash is purely related to both the browser plugins as well as the continued development of the creator programs. The end user can still download the older versions just fine and use them locally, there just won't be any new updates to either of those. Since the Adobe Flash Player parts are compliant with Windows 10 they will likely continue to work for natively on windows for a decade or two at least.
How to get and use the standalone Adobe Flash Player Projector:
1.) Visit the Adobe Flash Player Debug Downloads
2.) Click "Download the Flash Player projector" and save the executable to your computer
Optional: Move the executable to a directory that you're less likely to empty on accident so you don't lose the thing
3.) Run the executable, click "File", click "Open...", select the flash file you want to start and open it.
Optional: You can set the projector as default for opening all flash files by following the below steps:
1.) Right click a flash file
2.) Select "Open With..."
2.5) If it already has an association this might change to "Choose Another App..." instead
3.) In the newly opened dialog box click "More Apps"
4.) Scroll down to "Look for another App on this PC" and click it
5.) Navigate to your Flash Player Projector executable and select it
6.) Click "Open".
All flash files should now have their icon replaced from a white rectangle to the Flash Player icon, and when double clicked directly open the file in the projector.
Updated by Mairo