Whisk coconut milk, curry powder, fish sauce, sugar and salt and pepper to taste in bowl.
Pound chicken breast to 1/4-inch thickness in large resealable plastic bag. Pour in the coconut milk mixture and marinate in refrigerator at least 2 hours and up to overnight.
Preheat grill to medium hot and cook chicken, flipping as necessary, until browned and cooked through, about 5 minutes per side. Cool slightly; chop into thin strips.
Generously spread 1 side of each flatbread with virgin coconut oil. Spread layer of peanut butter on other side of 1 flatbread. Drizzle Sriracha over peanut butter; sprinkle basil over evenly. Layer on chicken strips. Drizzle sweet chili sauce over and top with cheese. Top with other flatbread, coconut oil-side-up.
Transfer carefully to preheated skillet and cook over medium-low heat, flipping halfway through, until bread is golden and crisp and cheese is melty. Cut into quarters to serve.
