Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Combine sweet potatoes, quinoa, trail mix, golden beet, red beet, flour, bread crumbs, oil, onion, parsley, tamari, sea salt, garlic, and red pepper flakes in a large bowl. Mix by hand until burger mix is thoroughly combined.
Divide burger mix into 10 portions; press each one firmly into a patty. Place on the prepared baking sheet.
Bake in the preheated oven until golden brown, about 20 minutes.