Add chicken, chopped onion, garlic, thyme, red pepper flakes, and bay leaves to pot. Then add water and lock lid. Cook for 35 minutes at high pressure.
Meanwhile... prep and chop all other veggies.
Once cook time is complete, allow pressure to release naturally for about 30 minutes. If there is any pressure left at that point, go ahead and quick-release remaining pressure.
Remove chicken and transfer to a large bowl. Remove meat from bones in large pieces. Discard skin and bones.
Pour broth through a fine mesh strainer. Discard cooked aromatics.
Add 6 cups of broth to pot, along with salt, tomatoes, potatoes, carrots, diced onions, and celery. (Reserve extra broth for another use.) Mix well, lock lid, and cook for 5 minutes at high pressure. Once cook time is complete, quick-release pressure.
Remove lid, then add chicken and gently mix well.