This is well known, but there are a few refinements that can be useful.
First, connect a USB stick, here it is identified, fdisk -l as /dev/sdc. Go to the download directory and boot the ISO image with kvm, connecting the stick. (Here 1024KB memory is used, Knoppix can run with less.)

sudo kvm -cdrom KNOPPIX_V7.6.1DVD-2016-01-16-EN.iso  -hdb /dev/sdc -m 1024 -boot d &
Boot Knoppix as a virtual machine, at the boot prompt write knoppix or knoppix64 + cheatcodes (keyboard=... for instance)
Inside the virtual machine, check that everything works fine. You should have internet connection, for example.
Use the 'Install KNOPPIX to flash disk' to install to the USB stick. Inside the VM, it is considered a hard drive and called /dev/sda, but from the size you can see that the correct drive is referenced. You may also create at persistent store at this time.
It takes some time, but after a while, you will get the message that the installation is complete.
Then it is time for powering down the ISO VM.
The preparation of the new Knoppix version can be continued by running the flash in kvm:

sudo kvm -hda /dev/sdc -m 1000  -boot d &
With persistent store in place, you can use synaptic, aptitude or apt-get to update or install packages. Don't forget to update the package listings!
It takes a bit more time to do installs in the kvm VM, but you can continue with your usual tasks on your pc in the meantime, so at least for me, this is a timesaver.
After having updated/installed the most important packages, you can shut down the VM, and copy the knoppix main directory from the USB stick to the pc. If there are already Knoppix directories there, give it a suitable name, like KNOPPIX761_0 (The _0 suffix is in case you, like me, will do remasterings.)
To boot the new version, you will have to modify the bootloader.
I use old, legacy GRUB, where this is very easy - but enough for now