In the pot of a multicooker, combine coconut milk, Greek yogurt, garlic, ginger, cumin, smoked paprika, turmeric, and salt; whisk to combine thoroughly. Place chicken thighs in the pot, dredging them in the coconut milk mixture.
Close Instant Pot lid and seal according to the manufacturer's directions. Cook on HIGH pressure for 30 minutes (chicken should reach 165° F.) Allow pressure to release naturally for 5 minutes; then use quick release to completely release pressure still in the pot.
Remove chicken thighs to a work surface and shred using 2 forks. Return shredded chicken to pot; stir to coat.