In a large bowl, mix pork, soy sauce, chives, vinegar, cornstarch, ginger, garlic, red pepper flakes and sesame oil until fully incorporated.
Using your finger, wet the edges of wonton wrapper with water. Place half a tablespoon of pork filling in the center of the wonton wrapper. Fold wonton in half diagonally to create a triangle, and seal the edges. Fold the two identical corners in on each other and press again to seal. Repeat until all wonton wrappers are filled.
Bring all soup ingredients to a boil. Simmer on low for 10 minutes, then remove ginger and garlic cloves and bring it back to a boil. Lower in wontons and cook for 10 minutes more. Serve into bowls and garnish with green onions and olive oil.