Mix together the cream cheese, mayonnaise, and sour cream in a large bowl. Fold in the chopped artichoke hearts, spinach, shredded parmesan, salt, garlic powder, and red pepper flakes. Set aside.
Cut each roll into fourths. Then roll each fourth into a rope. Flatten each rope with a rolling pin into a long, skinny oval about 4 to 5 inches long.
Grease a mini tart/muffin pan with baking spray. Criss-cross two pieces into the center of each mini cup, leaven the ends sticking out like flower petals.
Scoop a large spoonful of the spinach artichoke dip in the center of each cup. Repeat with remaining dough and dip until you get 24 blooming spinach artichoke cups.
Let the dough puff up a little bit, about 15 to 25 minutes. Then bake at 350 degrees Fahrenheit for 20 minutes or until the dough is golden brown on the petals and the bottoms of the cups, checking that the dough touching the dip is cooked through. Serve warm.