There are a few references (mostly web sites selling "natural" products) that confidently claim that kaolin is packed full of minerals. It seems, however, to be made up of about 85% to 95% kaolin: a phyllosilicate that is entirely silicon and oxygen. Nothing wrong with that, per se. But it isn't going to do you or your hair a power of good.
Amongst the other 35 ingredients, there is acacia gum. The description on Amazon.com is a little confused as to whether this comes from Chad or Senegal. Granted they are both countries in Africa, but geographically they are about as proximate as Houston, Texas and Albany, NY. Acacia gum's more common name is gum arabic and it is still the most important ingredient in chewing gum and shoe polish. In food, it is used as a stablizer. As an amusing aside, the appellation gum arabic has been largely dropped in favor of acacia (the tree from which it comes) because of some spurious association between the gum's production in the Sudan and Osama bin Laden.
Apart from all of that, wheat extrac, honey and a few botanicals, Aveda Volumizing Clay Conditioner has most of the things you'd expect to see in a high street hair care product: behentrimonium methosulfate (a detangler); babassuamidopropyl betaine (foam booster and thickener that usually comes from palm); various chemicals for 'easy combing'.
There are a couple of potential irritants such as benzyl benzoate and methylchloroisothiazolinone. In high concentrations, the latter, can cause chemical burns and is a skin and membrane irritant. It was largely removed from most cosmetic products except for those with only short duration skin contact such as rinse-offs. Its inclusion in certain forms makes it more acceptable to sensitive users, so it can be found in cosmetic creams and lotions which require skin contact. In the US accepted concentrations are 15 ppm in rinse-offs and 8 ppm in other cosmetic.