Add the smoked turkey necks to your pressure cooker. Add ½ cup of water to the turkey necks, then pressure-cook for 30 minutes. The turkey meat should fall off the bone. Remove the bones from the pressure cooker.
Add the collards, garlic, chicken broth, onion, and red pepper flakes to the pot with the turkey neck meat and water. Stir to combine, then pressure-cook again for 25 minutes, or until the collards are tender and have deepened in color.