The kernel tar archive contains both the kernel and the modules.
When you install the kernel without ubiboot, you do not copy the kernel to the device, but instead you need to have it on your linux/windows/mac computer that you are using to flash it.
The modules in the tar archive, however, need to go to the specific folder inside the device.

This is the reason for the advice "first untar the kernel archive on the device and then copy the kernel to your PC from /boot/"
(but of course you can also untar the archive also on your PC and get the kernel from there, no need to copy it off the device... )

Okay... so first thing is to untar the archive, and that command was already posted above.

Next thing is to resolve the module dependencies. Unless this step is done correctly, the kernel does not know which modules it needs to load together for a feature set, which means again that your device won't boot up.
And as was also mentioned, you need to do this step of course before you flash the kernel.
How to do that; go to the directory that contains the modules you just unpacked, "/lib/modules/2.6.32.61-plus". (needless to say, this is done on terminal and as root)
Give the command "/sbin/depmod -a 2.6.32.61-plus"
Check that there is created a bunch of files starting with module* (there should be about 11 of those if I remember correctly)

Last thing is the kernel flashing. For this you need flasher version 3.12.1 just as you noted yourself. In addition you need the correct firmware.bin file for your device, and I assume now that you propably have it if you have ever before flashed the device.
The firmware file is needed becuse the flasher needs to extract from it the remote flashing counterpart called the APE which actually is another small self-contained linux filesystem that knows how to flash the device...
Flashing is done the usual way; first power off the device, then give the flasher command and last step is to connect the device in USB.
The flasher command you should use is this:
sudo flasher -a firmware.bin -k zImage_2.6.32.61-plus-20131128 --flash-only=kernel -f -R

That's it, really. Now your device boots up with your new kernel.