And it is necessary to remember the instructions, because Adobe will surely update its Flash Plugin in between two Knoppix releases, and installing the new version via the native Knoppix method might not work, like it didn't presently.
First of all - Knoppix is a Live Linux. See also my warnings at Hardware install Wiki.

If you need an OS with security updates, you have to think about it, if Knoppix is the right one.

But if you want a new version of Adobe flash player within Knoppix you can do it with aptitude. "aptitude update" and if there is a new version of "flashplugin-nonfree" you can install (update) it. For example within Knoppix V7.3.0 there have been flashplugin-nonfree 1:3.4. After "aptitude update" I can select flashplugin-nonfree 1:3.5 and will get the latest version from Adobe.