​A follow-up to my original post.

I think the problem may have been related to all the Fedora updates
that have been installed since the last time I logged in.

When I logged out and logged back in I found that I was now
updated to using Firefox 57.0 (rather than the 56.0 I reported about.)
And Flash is now working.

So, I suspect there was some sort of mismatch somewhere in something
the already running Firefox dynamically loaded that caused the problem.

So the problem is now gone.
Thanks for your time, and sorry for the interruption.