In a medium bowl combine the lemon juice, garlic, red pepper flakes, salt, and pepper. Slowly whisk in the oil.
Season the calamari with the salt and pepper and place on a sheet pan with 2 tablespoons of the dressing. Toss to coat and marinate at room temperature for about 30 minutes.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Brush the cooking grates clean. Making two rows, place about 4 calamari tubes in a line over direct high heat so they can be weighted under the bricks. Place the bricks on top of the tubes, with the smooth side of the foil facing down, and grill, with the lid closed as much as possible, until the tubes easily lift off the cooking grate, about 2 minutes. Wearing barbecue mitts and using tongs, carefully tilt the bricks onto their sides off of the tubes. Turn the tubes over, and set the bricks back in place over the tubes for an additional 2 minutes. Transfer the tubes to a platter. Repeat with the remaining tubes, brushing the cooking grates clean after you remove the first batch. Grill the tentacles beside the bricks for about 4 minutes, turning once.
Put the tomatoes and onion into the bowl with the remaining dressing and toss to coat. Spoon the tomatoes and diced onion over the calamari tubes and add the avocado. Sprinkle with the oregano.