Measure the cereal into a very large mixing bowl and set aside. Line a large baking sheet with parchment paper.
In a microwave-safe bowl, combine the white chocolate chips and butter. Microwave in 30-second intervals, stirring after each, until completely melted and smooth, about 90 seconds total.
Let the melted chocolate cool for 2-3 minutes, then whisk in the dry cake mix until no lumps remain and the mixture is smooth.
Pour the white chocolate mixture over the cereal and gently fold with a rubber spatula until every piece is evenly coated.
Transfer the coated cereal to a large resealable plastic bag or a very large bowl. Add the powdered sugar, seal the bag, and shake vigorously for 1-2 minutes until all pieces are covered in a white coating.
Spread the puppy chow onto the prepared baking sheet in a single layer. Immediately sprinkle the rainbow sprinkles over the top while the coating is still slightly tacky.
Let cool completely at room temperature for 15-20 minutes until the coating hardens. Break apart any large clusters and transfer to an airtight container.
