Place an oven rack in the lower 1/3 of the oven. Preheat the oven to 400 degrees F. Line 2 baking sheets with parchment paper.
Place the pastry on the prepared baking sheets. Using the tines of a fork, prick the top of the pastry all over. Cover the pastry with parchment paper and place another baking sheet on top. Bake for 25 minutes until golden. Remove the top baking sheets and parchment paper. Set aside to cool.
Preheat a grill pan or preheat a gas or charcoal grill. Season the chicken with salt and drizzle with olive oil. Grill until the chicken is cooked through, about 5 to 6 minutes on each side. Set aside to cool.
In a small bowl, mix together the mayonnaise and cayenne pepper.
To assemble the Napoleons: Place 4 pieces pastry on a work surface. Slice each chicken breast diagonally into 6 (1/4-inch thick) slices. Place 3 chicken breast slices on each piece of pastry. Place 1/4 cup of spinach and 1 avocado slice on top. Spread 1 teaspoon of the mayonnaise mixture on the underside of another 4 pieces of pastry to create the middle layer of each Napoleon. Place on top. Repeat the layering. Each Napoleon should be completed with a piece of pastry as its top.
Arrange the Napoleons on a platter and serve.