Pour water into Instant Pot. Toss chicken, cut potatoes, salt, pepper, rosemary, thyme, oregano, red pepper flakes in a bowl until coated. Dump the mixture into a steamer basket.
Remove steamer basket. Discard water. Dump contents of the basket in. Add olive oil, lemon juice, parsley, oregano, cucumber, tomatoes, red onion, salt and feta. Toss well.