For the bars: Combine the Gluten-Free Multi-Purpose Flour, oat flour, maple sugar, flaxseed meal, oats, salt and cinnamon in a food processor and pulse until mixed. Add the butter and vanilla and pulse into coarse crumbs. Pulsing, add 5 tablespoons water until the dough comes together. Divide the dough in half and wrap each piece in plastic wrap, pressing down gently to flatten. Refrigerate until firm, about 30 minutes.
For the filling: Meanwhile, combine the dried berries and boiling water in a small bowl. Let stand until softened, about 15 minutes. Drain the berries, reserving the liquid. Place the berries in a blender or food processor. With the machine running, add the liquid, a little at a time, until a thick mixture forms.
Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper. Lightly beat the egg white with 1 teaspoon water in a small bowl. Lightly sprinkle a piece of parchment paper with the Gluten-Free Multi-Purpose Flour. Working with one piece of dough at a time, roll the dough on the floured parchment into a 4-by-12-inch rectangle, about 1/4 inch thick. Trim the edges. Leaving a 1/2-inch border and working lengthwise, top the center of the dough with half the filling. Fold the top half of dough over to cover most of the filling; brush the edge of the dough with the egg wash. Fold the remaining dough over to form a log, pressing down gently to seal. Gently flip the log so it's seam-side down; brush with the egg wash and sprinkle with flaxseed meal. Cut the log evenly into 3 bars and refrigerate. Repeat with the remaining dough, filling, and flaxseed meal.
Place the bars on the prepared baking sheet. Bake until lightly browned, 12 to 15 minutes. Slide the bars on the paper onto a rack and let cool completely.