Place blueberries in a food processor; pulse until finely chopped but not pureed. Mix blueberries, ground beef, flax meal, salt, and pepper together in a bowl; form into 12 burger patties. Freeze until patties are firm, about 10 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Cook burgers on preheated grill until no longer pink in the center and the juices run clear, 3 to 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).