Pour your bone broth into the dutch oven and then place your chicken into the broth. Bake at 350 degrees for 30 minutes. Alternatively, you could roasted a whole chicken and use that for this soup.
While chicken is cooking dice your onion, chives and zucchini.
Heat a cast iron skillet on medium-high heat. Once preheated, add olive oil. Once oil is preheated, add onion and zucchini and saute for about 5 minutes (until just starting to brown). Add garlic into cast iron with veggies and stir to incorporate for about 1 minute. Turn the burner off.
Remove chicken from dutch oven and place in a stand mixer with a flat beater attachment and turn on medium to low speed to shred the chicken (use forks to shred chicken if you don't have a stand mixer). If using a whole chicken, just tear off the chicken from the bones and toss it in your soup.
Keep the bone broth that you just cooked the chicken in inside the dutch oven. Turn the burner on high and boil the bone broth.
Once boiling, add the gnocchi and cook according to package (usually just a few minutes until it floats).
Turn the heat off and add the shredded chicken, zucchini/onion mixture, lemon juice, 3/4 of your chives, salt, pepper and red pepper flakes and stir.