Kodak does indeed sell a Kodachrome kit, but it is a complex mixing job I understand. Our labs mixed it from scratch.
The color developers are high pH and contain both developer and coupler. Therefore, as they keep they turn cyan, magenta and yellow. What else. And, control is a beast with the system.
It must run constantly with good replenishment or it goes out of control and drifts. It takes over 1 hour to process it, but it was routinely done by hand at Kodak.
The film has 9 emulsions and at least 6 layers, but I've forgotten most of it. I do remember that it is very very thin and is essentially a set of B&W coatings layered on top of each other that respond to the process to create the color. You can duplicate this by making tricolor positives on 3 sheets of any good pan film, and running them through a Kodachrome type process and then sanwiching them together.
In that case, the developers can be simple C41 or E6 type developers (depending on pos or neg) and the couplers can be rather simple organic chemicals just for demo purposes. (If you don't want exact color and good dye stability). This is a straightforward process to accomplish.
Yes, I am one of the co-inventors of the CD-6 used in Kodachrome. It was also to be used in E6 and in RA (EP-2 originally), but lawsuits again intervened from Ansco and Pavelle, and so the plans were cancelled for everything but Kodachrome.
The dye stability was much better with CD-6 under some conditions tested and the development reaction was faster. But, here we are without it now due to those law suits which claimed that Kodak changed the process to hurt competition. Well, our concern was not the competition, but rather the quality of the final image. We were very discouraged over that.
PE