Knoppix is a Live CD or DVD, so options for installing more applications are limited
Limited, but increasing. With Knoppix 5.01, because of the use of unionfs, it is possible to add a lot of applications to Knoppix, without the use of klik, and without needing to install to hard drive. I have done this lots of times, and added lots of debian packages. The added new apps go into ram, and will, of course, only last for the session, unless a persistent image is created.

I think this unionfs feature should be highlighted, because it will help people avoid being driven to the hard drive install in the mistaken belief that that is the only way to install new apps.

However if your Knoppix kernel is 2.4.xxxxx, you are probably using an older version of Knoppix which I am not familiar with, and may be does not use unionfs. You need to use Knoppix 5.01 to introduce new apps without the new for a hard drive install.

With Knoppix 5.01, adding flash and jre is quite straight forward. Go to the firefox plugins page and download the flash and jre package. Extract the flash package somewhere e.g. your desktop. Using a root shell, navigate to the location of the files and just do:

./flashplayer-installer

With sun jre, it is a single executable, just navigate to the location of the file and do:

./sun-java5-jre_1.5.....(complete the name of the file)

Good luck.