For the vinaigrette: Add the grapefruit juice and vinegar to a medium bowl. Add the olive oil while whisking to combine. Season with a pinch of salt and pepper.
For the calamari salad: Mix together the oil, chili flakes, garlic, lemon juice and zest, parsley and some salt in a large bowl. Add the calamari, toss together and let marinate for 20 minutes or up to 1 hour.
Preheat a grill to high heat.
Remove the calamari from the marinade and skewer them. Skewering the rings of the calamari onto 2 skewers each will help to keep them on the skewer and not fall off into the grill. Sprinkle with salt and pepper, and grill for about 2 minutes per side. They should be slightly charred and opaque.
Add the calamari, arugula, grapefruit segments, fennel and vinaigrette to a large bowl and toss. Season with salt and pepper and serve immediately.