Turn your Instant Pot to Sauté mode. Add olive oil, then stir in the diced onion, carrots, and celery. Cook for about 3–4 minutes until softened. Add the garlic and sauté for another 30 seconds until fragrant.
Add in the diced potatoes, diced tomatoes (with juices), shredded chicken, chicken broth, Italian seasoning, crushed red pepper flakes, salt, and black pepper. Stir to combine.
Cancel Sauté mode. Secure the lid and set the Instant Pot to Manual (High Pressure) for 6 minutes.
Once cooking is done, quick release the pressure. Open the lid and stir in the uncooked ditalini pasta.
Turn Instant Pot to Sauté again and cook uncovered for 8–10 minutes, stirring occasionally, until the pasta is tender.
Adjust seasoning if needed. Ladle into bowls and serve hot with crusty bread or a sprinkle of Parmesan cheese if desired.