@perknh: Sorry for keeping you waiting, my friend! It's been a busy day for sure! I must say, now finally it is starting to make sense to me
Let's see...
-
The version of Opera that I am currently running is reported as follows:
Version: 37.0.2178.32 - Opera is up to date
Update stream: Stable
System: Ubuntu 14.04.4 LTS (x86_64; Unity)
-
Yes, I did reboot and check if it is working, but it is not
Also tested by some flash-requiring applications that my Chromium can run, but Firefox and Opera cannot.
Here is my own analysis:
-
"adobeflash-plugin" indeed does prevent "pepperflash-plugin" from working properly. Whereas the former is installed, the system automatically prefers it over the latter one. Could this problem be overcome? Perhaps. For example, if you see the "Install Pepper Flash for Chromium in Ubuntu" instructions (www.webupd8.org/2013/04/install-pepper-flash-player-for.html), their attempt is to create a gedit file for the browser to use pepperflash as its default settings. Maybe this could be used for the Opera browser as well. However, that didn't work in my case with my Chromium.
-
Now, let's have a quick chronological overview:
First, the only browser I had was Firefox
Second, I installed the Chromium browser to my Linux Ubuntu 14.04 LTS system
Third, @perknh helped me to install pepperflash-plugin here at the Opera forum; this included purging all the remains of "adobeflash-plugin"
Fifth, the "pepperflash-plugin" started to work perfectly on my Chromium
Sixth, I installed the Opera browser; MY ASSUMPTION is that the Opera browser comes with "adobeflash-plugin" that does prevent "pepperflash-plugin" from working properly (which takes us back to square ONE)
Seventh, as said in the sixth step indeed, the "pepperflash-plugin" in my Chromium DID STOP from working. HOWEVER, Opera now displays this bugged flash version "99.xxxxxxxxxx" etc.
Eight [after a lot of hassle...], I finally re-purged the "adobeflash-plugin". The result is two-fold: 1) Opera (opera://plugins) ceases to display flash of ANY SORT, whereas 2) Chromium starts to show the up-to-date flash version AGAIN!
So in my strongly newbie analysis, I've reached a conclusion that "pepperflash-plugin" and "adobeflash-plugin" indeed compete against each other. Now I am just guessing, but I'd assume that the former would already include the latter, or at least be a modification of the latter. If there are two competing plugins on the system though, the system needs to select one.
Now recall back to the text file, the gedit file they were telling to create in one of the installation instructions. Wouldn't it make sense that the file is ought to be created TO DEFINE THE PREFERENCE ORDER of the existing plugins for the browser (in this case Chromium, but why not for Opera too)??
Well, as I said in my case, it didn't quite work as such for me, but on the other hand I had already removed all the rivalling competitors ("adobeflash-plugin", and there was also this "skunk") 
Well, these are just newbies thoughts.
Ps. Thanks for the distro-update command
It might solve the problem as well; actually I was waiting till the update can be carried out through an installed, but now after having played with the console a little bit - thanks to you - I think I might do it right now.