The secret to making this soap is to pour and tilt your loaf mold. Let the color set up and then liberally spray with rubbing alcohol (helps the next layer to adhere), and then, pour your next color while tilting the mold. You will need to prop the mold while pouring. I am sure you can find something around the home or workplace to make it work.
The biggest obstacle with this project (which, BTW, is considered a more advanced soaping technique) is making sure that you pour each color at the RIGHT time. The prior soap layer must be set up enough to accept the next color pour, but not too hard that it will refuse to accept it. That's where the rubbing alcohol is a big helper. It helps grabs and adhere to the next color pour, however, you still need to time your pouring.
Would love to see photos of your work using this pouring technique!