How can I create this coconut milk, fruit, and veggie snack at home?
Ok I'm going to give this a shot by helping you understand why the ingredients are in there. At it's core this seems to be a very aerated meringue with stabilizers to help avoid using dairy products and eggs. 


  organic sweet potato, organic apple puree concentrate, organic sweet
  pea, organic white grape juice concentrate


These ingredients are your base flavors, they seem to be a pretty simple mix of naturally sweet ingredients to bring the sugar content up. 


  organic coconut milk, organic guar gum, organic tapioca starch, xanthan gum


These ingredients are going to likely be added together first to hydrate the gum and the tapioca starch is going to act as a bulking agent to make it have more volume without being dense. The guar gum and xanthan gum are going to give a more consistent mouthfeel and flavor release and add some stability to the meringue. These two hydrocolloids together have a synergistic effect and will strengthen the overall product, allowing it to take on more air without collapsing. 


  organic spinach, natural flavor, malic acid, ascorbic acid (vitamin
  C), B. coagulans, pre and probiotics, organic kiwi, organic cinnamon


These final ingredients appear to be flavor enhancing or balancing. Malic acid is very tart as is kiwi, the cinnamon likely helps to balance this. Ascorbic is likely in there as an antioxidant to prevent discoloration and the rest look to be the pro-biotics that are touted in the packaging but really probably play very little part in the making of the food. 

I believe the process of making this will be very similar to this recipe here 
http://blog.ideasinfood.com/ideas_in_food/2007/04/whipped_yogurt_.html