Beat the egg whites with the sugar until frothy and add in the coconut butter and flour. Divide the batter between 3 bowls (50%, 25%, and 25%) and add pink, green, and yellow food coloring in that order.
Line 2 small baking sheets with parchment paper, transfer the pink batter to one of the sheets, and smooth it out. Use the other baking sheet for the green and yellow batter (you'll need a little more of the green batter). Smooth them out as well and then bake both baking sheets at 275°F for 15 minutes.
Take the baking sheets out of the oven and let them cool. Use a cookie cutter to cut flowers from the pink batter. Then use a straw to create a hole in the center of each flower.
Use the leaf-shaped cookie cutter to cut leaves from the green batter and use the straw to cut small circles from the yellow batter. Assemble the 3 parts into flowers on a large baking sheet lined with parchment paper.
Beat the egg whites with the sugar until frothy and then add the coconut butter and flour. Carefully spread the batter over the flowers on the baking sheet. Smooth everything out, transfer the pan to the oven, and bake at 275°F for 15 minutes. Let the baking sheet cool a bit and flip it over onto a clean dish towel.
Carefully remove the parchment paper and use a second towel to flip the cake to the other side (the side with the flowers should be facing down).
Sprinkle sugar over the cake. Combine all the ingredients for the cream cheese frosting and spread it over the cake, leaving a little room near the top. Place the strawberries in rows of 5 on the cake and pipe the rest of the cream cheese frosting in between the rows.
Use the dish towel to roll up the cake and refrigerate it for about 90 minutes.
