To update your pepperflashplugin type
sudo apt-get update
sudo apt-get install --reinstall pepperflashplugin-nonfree
Then check, if you have the newest version here: http://www.adobe.com/software/flash/about/
Simple sudo apt-get upgrade will not update it.
Thank you, I've been scratching my head for a while trying to get Flash to work on Opera 39 (Linux). The pepperflashplugin has to be reinstalled because during installation because the package is just a downloader/installer that runs a download script to download the latest version. For this reason the normal apt-get update/upgrade will not work, as it will not see an updated downloader.