Kiln seems to be installed and enabled. At least that's what systemctl list-unit-files --type=service | grep kiln suggests, which shows "kiln.service enabled". I have rebooted several times, but typing http://localhost:8000 in Firefox always tells me "Unable to connect". What could be the cause of this? Ubuntu is based on Debian, so the .deb file should work. I first tried installing it via dpkg, but that failed. I think it was a dependencies issue, since using gdebi seemed to solved the issue. Could it be, that I still need to hand-install some Ubuntu specific stuff for it to run in my browser?
Version 0.5.1 of Kiln has a Debian package (.deb) that, ironically, doesn't work on Debian. It only works on Ubuntu. This is because Ubuntu enables user namespaces by default but Debian does not. You can manually enable them on Debian by following the "permanent" instructions here: https://unix.stackexchange.com/a/303214/197651
echo 'kernel.unprivileged_userns_clone=1' > /etc/sysctl.d/userns.conf
This should be fixed in an upcoming release by having the installer do this step for you.