You can boot into RedHat, mount the Slackware partition, then copy the Slackware kernel over.

You don't need to move the kernel with grub you just have to setup grub correctly. I currently multi-boot different linuxs all with seperate /boot partitions. Pay special attention to making sure the redhat system can fully see you slackware partition since it is the one that holds grub. Also pay close attention to your line in grub that refers to /boot. Here is an example of mine.

# For booting GNU/Linux
title Slackware-2.4.21-ac4
root (hd0,5)
kernel (hd0,1)/vmlinuz root=/dev/hde6 hda=ide-scsi mem=nopentium

# For booting GNU/Linux
title Slackware-2.5.73
root (hd0,5)
kernel (hd0,1)/vmlinuz-2.5.73 root=/dev/hde6 hda=ide-scsi mem=nopentium vga=0x31a

# For booting GNU/Linux
title Gentoo-2.6.0-test1
root (hd1,2)
kernel (hd1,0)/vmlinuz-2.6.0-test1 root=/dev/hdf3 hda=ide-scsi vga=0x31a

# For booting GNU/Linux
title Gentoo-2.5.74-mm1
root (hd1,2)
kernel (hd1,0)/vmlinuz-2.5.74-mm1 root=/dev/hdf3 hda=ide-scsi vga=0x31a

# For booting GNU/Linux
title Slackware-2.4.21
root (hd0,5)
kernel (hd0,1)/vmlinuz-2.4.21 root=/dev/hde6 hda=ide-scsi mem=nopentium vga=0x31a

You can see quite clearly here that I have slackware and gentoo's /boot partitions in different places.

For your Slackware Grub entry you have a spelling error

title Slackware
root (hd0,5)
kernel /boot/vmlinuz-ide-2.4.20 root=/dev/hda6 ro

this works for me

Change your kernel line for slackware to read

kernel (hd0,5)/boot/vmlinuz ro root=/dev/hda6 hdd=ide-scsi