In a large bowl, combine the sugar cookie dough, sprinkles and flour until well incorporated. Transfer to a 9x13-inch baking pan and press down into an even layer.
Bake until golden brown around the edges and the center has just set, about 10 to 12 minutes. Let cool completely.
Beat the cream cheese, sugar and milk until well combined. Stir in the frozen whipped topping. Pour over the sugar crust and set in the fridge until ready to use.
Place the strawberry jell-o in one large bowl, and the lime jell-o in a second bowl. Pour 1 cup boiling water into each bowl and stir until completely dissolved. Stir 3/4 cup cold water into each bowl and refrigerate both for 45 minutes.
Transfer the green mixture into the baking dish, over the cream cheese layer and spread out evenly. Chill for 15 minutes.
Stir in the strawberries into the strawberry jell-o and then pour over the green jell-o layer and spread out evenly. Chill until firm, about 1-2 hours.
Cut into bars and serve with a dollop of whipped topping and sprinkles.