Heat a grill or grill pan to medium-high or prepare coals.
Combine herbs, garlic, red pepper flakes, fennel, salt, pepper and about 1/3 cup olive oil; coat chicken.
Char bread on the grill on both sides; rub with cut garlic clove and drizzle with oil. Sprinkle with flaky sea salt and chop into bite-sized pieces.
Grill chicken 12 minutes to cook through, turning once. Grill halved lemon 4 minutes to char. Douse chicken with charred lemon juice; slice or chop into bite-sized pieces.
Grill 2 more halved lemons for 4 minutes for the salad. Juice the lemons into a large bowl and add the pasted garlic, vinegar, honey or sugar, fennel fronds, salt, pepper and whisk in about 1/2 cup olive oil. Add the fennel, celery, onion, peppers, tomatoes, olives, baby bitter greens and bread, and toss to combine. Add half the chicken and toss, arrange the rest of the chicken on top of the salad and serve.