For this experiment, I am recording my findings here.
This experiment is simply an extension of the "Golden Rain" experiment. For "Golden Rain", in short, you mix lead nitrate and potassium iodide (two clear, colourless solutions) and get a precipatation reaction. It forms potassium nitrate (colourless solution) and lead iodide (yellow solid). When this is heated and then cooled, the lead iodide crystalises and form glitter-like fleck of gold. "Scientific Rainbow Glitter" experiment takes this to another level, attempting to make not only yellow glitter, but a full rainbow. But that's easier said than done.
The first problem was to predict whether a chemical reaction was a precipitation reaction. I couldn't just mix random chemicals, because I'd probably make some sort of poisonous gas. The way to do this is with the Solubility Rules Table (left). A precipitation reaction, like "Golden Rain", is a reaction that is liquid + liquid => liquid + solid. With the Solubility Rules Table, we can determine chemical reactions with this result, e.g. AgNO3(aq) + KI(aq) ==> AgI(s) + KNO3(aq). This reaction is detailed under The Silver Iodide Conundrum)
The next problem was that not all precipitates cystalise, and trying random precipitates could be quite inefficient. While trying to question the elusive Mr. Bruce about this, I used brute force and tried to look for patterns. This work is on the experiment data spreadsheet (the link is at the top of this page). This specific data is under Reactions and Hypotheses; Patterns. This data was not a waste of time, because as far as Mr. Bruce knows, there is not a method for predicting crystallisation.
I have given up on this experiment.