In a medium bowl, combine calamari, garlic, chile flakes, parsley, 1/3 cup oil, 2 tbsp. lemon juice, and 1/2 tsp. salt. Chill, stirring often, 1 to 5 hours.
Pour calamari and marinade into a colander over a bowl. Brush marinade over cut sides of bread; grill on each side over high heat (450° to 550°) until grill marks appear, 3 to 5 minutes. Cut into slices.
Grill calamari tubes, turning once, just until firm, 3 minutes. Meanwhile, using tongs, drop tentacles in clumps onto grill just to firm up, then spread out to cook evenly, 4 minutes total. Put calamari in a dish and drizzle with remaining oil, lemon juice, and salt. Serve with bread.