Heat the oven to 350°F. Line three 8-inch round cake pans with parchment paper and lightly coat the sides with neutral oil.
Whisk the cake flour, baking powder, and salt in a medium bowl. Stir the vanilla extract and almond extract into the soy milk.
Beat the dairy free butter, neutral oil, and granulated sugar for 3 minutes, until very light. Beat in the egg whites and whole egg in several additions, mixing well after each addition.
Mix in the flour mixture in three additions, alternating with the soy milk in two additions. Toss the rainbow jimmies with 1 teaspoon of the measured flour mixture before gently folding them into the finished batter.
Divide the batter among the prepared pans and bake for 21 to 25 minutes, until the tops spring back lightly. Cool the layers in the pans for 10 minutes, then transfer them to wire racks to cool completely.
Beat the dairy free butter for 3 minutes. Gradually beat in the powdered sugar, soy milk, vanilla extract, and salt until the frosting is light and smooth.
Stack the cooled layers with vanilla frosting between them. Frost the top and sides, decorate with the remaining rainbow jimmies, and let the cake set for 20 minutes before slicing.