In your instant pot, combine the chicken thighs, carrots, celery, onion, radishes, diced tomatoes, garlic, salt, rosemary, thyme, fennel seeds, + chicken stock. Stir to combine.
Close with the lid, and make sure the vent is at SEALING. Cook on HIGH PRESSURE for 15 minutes. Will take about 10-15 minutes to reach pressure, then it will start counting down from 15. After the 15 minutes is up, do a QUICK RELEASE, where you move the valve to VENTING to release all the steam. Once all the steam is gone and the float valve has dropped, you can safely open the instant pot.
Remove the chicken thighs. Discard the skin and bones, shred the meat. Return to the instant pot.
Add in the balsamic vinegar and spinach. Stir to combine. Taste for salt + pepper. Adjust if needed.
Serve warm.
Leftovers will keep in an airtight container refrigerated for at least 5 days, or frozen for at least 6 months.