Combine olive oil, lemon juice, ginger, and garlic in a large sealable plastic bag. Add chicken drumsticks and toss to coat. Allow to marinate for 20-30 minutes in refrigerator.
Cook chicken on grill over medium heat until cooked through, about 20 minutes or until meat thermometer reads 165°F Turn once halfway through.
While chicken is cooking, prepare the salsa. Gently remove the halved grapefruit pieces from the skin and place in a medium bowl. Add avocado, red pepper flakes, tomato, onion, yellow bell pepper, cilantro, and lime juice, and toss gently to combine.