Combine the chickpeas, salmon, onions, garlic, cilantro, cumin, salt and chili flakes in the bowl of a food processor and pulse until combined but still chunky, scraping down the sides of the bowl once or twice. Add the flour and baking powder and pulse until you have a soft mixture.
Roll the dough into meatball-sized balls and flatten each slightly, making a little patty.
Heat about 1/2-inch of canola or other mild vegetable oil in a heavy skillet until it’s hot but not smoking. Test with a bit of falafel mixture or a scrap of bread – the oil should bubble up around it. Cook the falafel for a few minutes per side, until golden and crisp. Transfer to a paper towel lined plate.
Serve warm, with tzatziki or thick plain Greek yogurt spiked with lemon, garlic, tahini and salt. Makes about 20 falafel.