It is possible to install other versions with update-pepperflashplugin-nonfree command.
If you list the contents of the script you will find options to install unverified, beta and unstable versions.
I think i tried unverified versions, but now I am back to stable I think. I am not sure because the status request is a bit, bah:
sudo update-pepperflashplugin-nonfree --status
Flash Player version installed on this system : 20.0.0.306
Flash Player version available on upstream site: 20.0.0.228

But at least it is possible to try
sudo update-pepperflashplugin-nonfree --install --beta (or --unstable/unverified)

-Tommy

My opera installation refused to run flash on nrk.no.

So I had to figure out to update the pepperflash plugin that I got through enabling the multiverse repositories and installing pepperflashplugin-nonfree 1.7ubuntu1.

In this bug report I found the command that updates the package outside the ubuntu update process:
https://bugs.launchpad.net/ubuntu/+source/pepperflashplugin-nonfree/+bug/1312219

To update:
sudo update-pepperflashplugin-nonfree --install

-Tommy

At last I found the solution, at least for people using the pepperflash plugin from ubuntu.

During installation of ubuntu gnome in October I added a repository (I cannot find the instructions anymore) that made the pepperflash plugin available as a separate package. This package does not seem to update, probably because the repository I added does not update.

But in a feature request for automatic updates I found the instruction to use some commands to update the plugin:
https://bugs.launchpad.net/ubuntu/+source/pepperflashplugin-nonfree/+bug/1312219

So, If you use this repo for the pepperflash plugin: https://launchpad.net/ubuntu/+source/pepperflashplugin-nonfree

Just write:
su
update-pepperflashplugin-nonfree --install

-Tommy