Sorry for asking: I just had to figure out how to page back. Anyway, I have discovered one answer to my original question, submitted on Aug 16th. I downloaded Flash Player, version 13, from the archive download site, and uninstalled the version(s) of flash Player on my computer. I was surprised that the downloaded version 13 came as an application ( .app) rather than with an installation screen such as when I try to install the upgrade, however I clicked on this version 13 application and then searched for videos. When I clicked on a video I first briefly saw the black screen with the message (I cannot remember what it says, but it is what you always see when it refuses to play a video). then, within a second, the black screen went away and the video played normally.
This is obviously a "kludge" but it works for me now, so that I can function. It may be helpful for others with the same or similar problems.
It would be still better if there was a way I could successfully install version 14.