In a food processor fitted with the metal blade, combine corn, water, lemon juice, thyme and salt. Process until smooth. Transfer to a bowl.
Add red pepper and ground flax seeds. Mix well. Cover and set aside for 10 minutes to allow the flax to absorb some of the liquid and swell.
Using a 1?4-cup (60 mL) measure, divide mixture into 4 equal portions and, using your hands, shape into round cakes. Transfer to a serving plate. Serve immediately or cover and refrigerate for up to 3 days.
To yield the maximum juice from citrus fruits, allow them to sit at room temperature for 30 minutes before juicing. Once the fruit is at room temperature, use the palm of your hand to roll it on the counter to release the juices before slicing and squeezing.
Use either golden or brown flax seeds for this recipe. Golden flax seeds will make the cakes lighter in color while brown flax will make them darker.