Preheat the broiler. Coat a broiler-pan rack with cooking spray.
In a cup whisk together the vinegar, olive oil, flaxseed oil, garlic, salt, and black pepper, and set aside.
Place the bell peppers, skin side up on the prepared rack. Broil, without turning for 10 minutes, or until skins are blackened and blistered in spots.
Place the peppers in a paper bag and seal. Let stand for 10 minutes, or until cool enough to handle. Peel the skin from the peppers and discard. Cut the peppers into 1/2" - wide strips.
Arrange the tomato slices on a platter. Place the cheese slices over the tomatoes. Scatter the pepper strips on top and sprinkle with basil. Drizzle the dressing over the salad. Let stand for at least 15 minutes to allow the flavors to blend.