Preheat oven to 350°F and line a baking sheet with parchment paper.
Lightly dust a clean work surface or cutting board with some of the 1/3 cup flour.
Remove the 16.5 oz refrigerated sugar cookie dough from its package and place it on the floured surface.
Sprinkle the remaining flour over the dough and knead the flour into the dough until it is well combined and no longer overly sticky.
Using a rolling pin, roll the dough into a rectangle about 14 inches by 10 inches and about 1/4 inch thick; add small amounts of the remaining flour from the 1/3 cup if the dough sticks.
Sprinkle the rainbow colored sugar in parallel stripes across the dough, leaving a thin (about 1/4–1/2 inch) bare strip along one long edge to help seal the roll.
Starting at the long edge opposite the bare strip, gently roll the dough into a tight log (like a cinnamon roll), then press the seam to seal.
Using a sharp knife, slice the log into 1/2-inch-thick rounds and place the rounds cut-side up on the prepared parchment-lined baking sheet, spacing them about 2 inches apart.
Gently press each cookie with the palm of your hand to flatten slightly.
Bake for 10–12 minutes, or until the edges are light golden brown.
Let the cookies cool on the baking sheet for 2–3 minutes, then transfer them to a cooling rack to cool completely.
Store cooled cookies in an airtight container for up to one week.