Hydrogen peroxide and ThickenUp (potassium chroride)
Hydrogen peroxide is an oxidizer and unstable.  It can react with a variety of common materials to exothermically release oxygen gas, exothermically oxidize the material, or both.  Additionally it can damage skin.  Fortunately these safety concerns are only really a major consideration at higher concentrations, where the amount of oxygen released can be problematic, and the heat is sufficient to pose a burning or fire hazard, made worse by the oxygen.  At lower concentrations (such as the 12% you're talking about), it poses mild hazard to skin, and significant hazard to clothes and eyes, but shouldn't present any major safety concerns.
The potassium chloride shouldn't do anything, but the hydrogen peroxide may react with the maltodextrin, or other unlisted ingredients.  To test for this, you can dilute down your hydrogen peroxide (or buy some medical hydrogen peroxide that is already lower concentration), and mix it with the TickenUp.  If bubbles or foam forms, that's an indicator that the hydrogen peroxide is reacting with the maltodextrin or some other ingredient in the TickenUp, and you shouldn't use it, because it will destroy your peroxide before it can bleach your plastic.
Of note, additional care should be taken to wash the plastic after using this form of Retrobright, because the maltodextrin and potassium chloride may leave an undesirable residue otherwise.  Additionally, the xantham gum is only required if you wish to apply the Retrobright as a gel, if you are planning on submerging the plastic, the xantham gum is unnecessary.