1. Put the all-purpose flour, rye flour, baking powder and salt in a food processor and pulse until blended. Pour the club soda into a measuring cup and add the vinegar. Pour the liquid into the processor as it is running and mix until the batter is very smooth. Let sit for 10 minutes.
2. Heat a 10-inch nonstick skillet over medium heat. Spray the skillet with a thin coating of nonstick spray. Make the injera the way you make a crepe: Remove the skillet from the heat and tilt the edge farther from you down toward the floor. Pour 1/3 cup of the batter in a pool slightly off-center further from you, and then quickly swirl the pan so that the batter covers the entire surface. Place the pan back on the heat, cover with a lid and cook until the edges start pulling from the pan and the top is shiny and slightly dry, 90 seconds to 2 minutes. Peel the injera from the pan and transfer to a plate, top-side up. Serve cool.