The package name will be “pepperflashplugin-nonfree”, but it is a free plugin.
Open the Terminal. Type sudo update-pepperflashplugin-nonfree –status and press ↵ Enter to check for updates. If the available update is a higher number than your installed update, there is an update available. Type sudo update-pepperflashplugin-nonfree –install and press ↵ Enter to install the update. Restart your browser to complete the update.
If Flash is broken in Chrome, try uninstalling and reinstalling it.
If you want to install the outdated version for Firefox, read on.