Heat a large skillet over medium-low heat. Add the 1/3 cup flaxseeds; cook, stirring with a wooden spoon, for 5 to 7 minutes or until the seeds pop gently. Cool seeds. Place seeds in a blender. Cover and blend until seeds are finely ground. (You should have about 1/2 cup.)
In a large bowl, stir together 1 cup of the all-purpose flour, the rye flour, and yeast. Add the warm water, oil, honey, and salt. Beat with an electric mixer on low to medium speed for 30 seconds, scraping side of bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in the ground flaxseeds and as much of the remaining all-purpose flour as you can.
Turn out onto a lightly floured surface. Knead in enough of the remaining all-purpose flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape dough into a ball. Place in a greased bowl. Turn once to grease surface of the dough. Cover; let rise in a warm place until nearly double in size (about 1 hour).
Punch down dough. Turn out onto a lightly floured surface. Cover; let rest for 10 minutes. Grease 2 baking sheets; set aside. Roll dough into a 16x8-inch rectangle. Brush dough rectangle generously with water. Sprinkle with the 2 tablespoons flaxseeds. Gently pat flaxseeds into dough. Cut dough crosswise into 1-inch-wide strips. Place strips 1 inch apart on prepared baking sheets; if desired, twist each breadstick two to three times. Cover; let rise in a warm place until nearly double in size (about 30 minutes). Meanwhile, preheat oven to 425 degrees F.
Bake breadsticks for 12 to 15 minutes or until golden brown. Remove from baking sheet. Cool on wire racks.