I found three different versions. Take a look, and try the recipe that appeals to you the most.
The first rainbow jello recipe calls for five boxes of Jell-O, unflavored gelatin, and condensed milk. This recipe seems the easiest of the three because you're alternating Jell-O with milk and you don't actually have to deal with the tricky bit of blending the colors to make a rainbow. To get the details, visit Momofuku for 2.
The second recipe I found via odeedoh. It calls for three different colors of Jell-O and a box of Knox Gelatin, and should look something like the photo above when completed. For the how-tos, visit Do Better.
The last recipe (result shown above) is from Adventures of a Food Slut, who used Jell-O, cool whip, and sour cream. For how-tos, visit her blog.
Have you ever made rainbow jello? What's your favorite recipe?