Line a 9-by-13-inch baking dish with foil, leaving a 2-inch overhang on 2 sides; coat with cooking spray. Whisk the all-purpose flour, cocoa powder, almond flour and salt in a medium bowl. Beat the butter and sugar in a large bowl with a mixer on medium speed until creamy, 2 to 3 minutes. Reduce the mixer speed to medium low; beat in the flour mixture until combined.
Press the dough evenly into the prepared baking dish in a thin layer with damp hands. Refrigerate until firm, about 30 minutes.
Preheat the oven to 350 degrees F. Bake until the chocolate layer is set, 25 to 30 minutes; let cool completely in the pan.
Meanwhile, combine the jam, dried cherries, lemon juice, cornstarch, almond extract and 1/4 cup water in a small saucepan. Bring to a simmer and cook, stirring occasionally, until the dried cherries soften and the mixture thickens, about 10 minutes. Spread over the chocolate layer and let cool completely.
Lift the bars out of the pan using the foil. Put the white chocolate in a microwave-safe bowl and microwave in 30-second intervals, stirring, until smooth; drizzle on the bars. Let stand until the chocolate sets, then cut into squares.