Preheat oven to 425°F. Pick over flowers and remove twigs or foreign matter. Rinse thoroughly in colander under cold water.
Fill medium saucepan with water and set to boil. Add hibiscus and turn off heat. Let sit about 3 minutes, until fully hydrated. Drain then rinse flowers again under cold water to wash away remaining grit. Set aside.
Heat butter and olive oil in heavy-bottomed skillet over medium heat. Add onion and chile and cook until soft, about 3 minutes. Stir in flowers and pinch of salt, and cook about 2 minutes, until evenly combined.
Add sugar and cook a few minutes more, stirring to coat. When flowers darken to deep-purple color, turn off heat.
Warm pita pockets lightly in oven or on gently heated comal. Cut open top half only, around edge of pitas, and tuck in layer of cheese slices. Top with layer of hibiscus flower filling. Place pockets on sheet pan in oven until cheese has melted, about 4 minutes. Cut into quarters and serve immediately.