In a medium bowl, combine the flour, salt, and baking powder and whisk until sifted. Add the flour mixture to the butter mixture about 1 cup at a time, stirring with the paddle attachment (not the whisk) to incorporate each cup. Do not over mix.
Divide the dough into six equal portions - it helps if you have a kitchen scale for this. Using gel food coloring (gel works so much better for vibrant colors than standard food coloring), color each layer a color of the rainbow. I used a hand mixer to combine the color in with each dough section and then rinsed the bowl and beaters before moving on to another color.
Place dough in individual ziplock bags or saran wrap and refrigerate until firm, about an hour or two. One at a time, roll colors into approximately 6x9 inch rectangles. Refrigerate each layer after rolling, and then add subsequent layers on top in rainbow color order.
When all layers have been stacked, trim edges for a neat rectangle. Wrap again in saran wrap and freeze until very firm. Slice strips across the 6 inch side about 1/4 inch thick and cut each strip in half. Place cookies on a parchment lined cookie sheet and freeze again (this helps minimize spreading).
When you are ready to bake, heat oven to 350 degrees. Roll dough out, cut out cookies, and bake for 6-10 minutes. Cool on the cookie sheet for a few minutes before transferring to a wirerack. Cool the cookie sheet in between baking each batch.
Leftover dough can be stored in the freezer for a few weeks.