Line a large baking sheet or two baking sheets with parchment paper and set aside.
In a microwave-safe bowl, combine 1 cup blue candy melts, ¼ cup creamy peanut butter, and ½ tablespoon vegetable oil. Microwave for 30 seconds, stir, then continue microwaving in 15-second intervals until the mixture is completely melted and smooth.
Place 4 cups Chex cereal in a large mixing bowl. Pour the melted blue candy mixture over the cereal and gently stir until evenly coated.
Add 1 cup powdered sugar to one gallon-size zip-top bag. Transfer the coated cereal to the bag, seal tightly, and shake until the cereal is completely coated. Spread the puppy chow onto the prepared baking sheet to cool completely.
Repeat the process by combining 1 cup red candy melts, the remaining ¼ cup creamy peanut butter, and the remaining ½ tablespoon vegetable oil in a microwave-safe bowl. Melt until smooth.
Place the remaining 4 cups Chex cereal in a large bowl. Pour the melted red candy mixture over the cereal and stir until evenly coated.
Add the remaining 1 cup powdered sugar to the second gallon-size zip-top bag. Add the coated cereal, seal the bag, and shake until evenly coated. Spread onto the prepared baking sheet and allow it to cool completely.
Once both batches have cooled, combine the red and blue puppy chow in a large serving bowl. Add 1½ cups red, white, and blue M&M's and gently toss to combine.