Actually, I found my own answer: klogd works with syslogd. Ubuntu uses rsyslogd which does not not need the klogd server at all. In fact, rsyslogd reads the /proc/kmsg file itself. So everything works as is with the default configuration from Ubuntu.

Trying to install the busybox-syslogd on my ubuntu machine broke its configuration: any nic interface was no longer showing up in ifconfig or ip link show, event after full reboots... I suggest to not install this package, unless you know what you're doing.