Coat a 3-quart slow cooker with cooking spray; set aside. In a large bowl stir together flour, flax seeds, baking powder, caraway seeds, sugar, salt, and baking soda. Make a well in the center of flour mixture; set aside.
In a medium bowl combine beer, sauerkraut, and mustard. Add beer mixture all at once to flour mixture; stir just until combined (batter will be sticky). Spoon batter into the prepared cooker, pressing batter to edges and smoothing top.
Cover and cook on high-heat setting for 3 to 3-1/2 hours or until a wooden toothpick inserted near the center comes out clean. Turn off cooker. Carefully remove lid so condensation from lid does not drip onto bread. Cover opening of slow cooker completely with paper towels; place lid on top. Cool for 10 to 15 minutes. Run a knife around edges of cooker; remove bread from cooker. Cool completely on a wire rack.