You do need the change the following:
image=/boot/vmlinuz
label="slack-linux"
root=/dev/hdb1
initrd=/boot/initrd.img
append="devfs=mount acpi=off quiet"
read-only
This will use the mdk kernel. You need something like
image=/mnt/slack/boot/vmlinuz {check what the exact name of the kernel is}
and
initrd=/mnt/slack/boot/initrd.img {again check what the exact name is; I actually don't use this for my slack isntall at all}
then run
/sbin/lilo -v
And you don't need to do anything to your slackware install.
Lilo gets installed once and you have to edit
lilo.conf in the distro from which you are isntalling
lilo into the mbr. In your case it is mdk and you are all set once you edit
lilo.conf in mandrake and run
lilo. This is what I have on my machine too so I know it works