Preheat oven to 375°.
Melt corn syrup and butter in a 10-inch cast-iron skillet coated with cooking spray over medium-high heat; remove from heat. Sprinkle with 1/2 cup sugar and pecans; arrange apple slices spokelike over brown sugar mixture, working from center of skillet to edge.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, flaxseed meal, baking powder, and salt, stirring with a whisk.
Combine 1/3 cup sugar, rind, vanilla, and eggs, stirring with a whisk. Beat egg whites with a mixer at high speed until soft peaks form. Add remaining 1/3 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Add whole egg mixture to flour mixture; stir just until moist. Gently fold in egg white mixture.
Spoon batter over apples. Bake at 375° for 30 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 5 minutes on a wire rack. Loosen cake from sides of pan with a knife. Place a plate upside down on top of cake. Invert cake onto plate. Cut into wedges. Serve with whipped cream. Garnish with cinnamon, if desired.