The line you should enter in /etc/syslog-knoppix.conf for kern.log is :
kern.* -/var/log/kern.log
And I think syslog should expose everything that dmesg command does, you just remove the minus sign - in fron of it.
All log files are disabled because they interfere with the screen reader, at least that is what /etc/syslog-knoppix.conf says, but I don't think you use screen reader