Heat an Instant Pot on the SAUTE setting. Add the olive oil to the insert, then the mushrooms, onion and garlic. Saute until golden.
Add in the celery and carrot, then stir in the Better than Bouillon.
Pour in the chicken stock, rice, and seasoning packet, then place the chicken breasts in the pot. Secure the lid, set the valve to Vent and turn on Soup mode for 20 minutes.
When Instant Pot is done, allow to naturally vent for 5 minutes, then manually vent the remaining pressure.
Add the butter to a 2 cup microwave safe measuring cup. Melt in microwave, then stir in the flour with a fork. Stir in cream.
Remove chicken breasts from the pot and shred. Pour in the cream/butter/flour mixture, along with the milk and shredded chicken and stir to combine. Replace the cover for 5 minutes to let the soup warm and thicken before serving.