Preheat the oven to 350 degrees F. Line three 9x13-inch baking pans with parchment paper and grease them lightly. In a large bowl, beat the almond paste, granulated sugar, and softened butter with an electric mixer until smooth and fluffy, about 4 minutes.
Add the egg yolks one at a time, beating well after each addition. Mix in the gluten free flour blend and fine sea salt on low speed until just combined.
In a separate clean bowl, beat the egg whites with an electric mixer until stiff peaks form, about 3 to 4 minutes. Gently fold the whipped egg whites into the almond batter in three additions, being careful not to deflate the mixture.
Divide the batter evenly among three bowls. Leave one bowl plain, tint one bowl with red food coloring, and tint the third bowl with green food coloring.
Spread each colored batter into one of the prepared pans in a thin, even layer. Bake all three layers for 10 to 12 minutes until the edges are just set and a toothpick comes out clean. Let the layers cool completely in the pans.
Warm the raspberry jam in a small saucepan over low heat until it is thin and spreadable. Place the green layer on a parchment-lined cutting board and spread half of the jam evenly over the top. Carefully place the plain layer on top and spread the remaining jam over it. Top with the red layer, pressing down gently.
Wrap the assembled stack tightly in plastic wrap and place a second cutting board on top to weigh it down. Refrigerate for at least 4 hours or overnight so the layers fuse together.
Melt the chocolate chips and coconut oil together in a microwave-safe bowl, stirring every 30 seconds until completely smooth. Spread half of the melted chocolate evenly over the top of the cookie stack. Refrigerate for 15 minutes until the chocolate sets.
Carefully flip the stack over and spread the remaining chocolate on the other side. Refrigerate for another 15 minutes.
Using a sharp tool, trim the edges to reveal the clean colorful layers, then slice into small rectangular cookies about 1 inch wide and 2 inches long. Store in an airtight container in the refrigerator.