Preheat the oven to 200F for keeping the quesadillas warm. In a medium pot, cover rosa de Jamaica with enough water to cover calyces by an inch. Bring water to a boil and simmer for 15 minutes, until petals are al dente. Drain calyces and leave them to cool for 10 minutes. Reserve liquid for another use, such as margaritas or granitas.
Chop calyces roughly.
In a medium saucepan over medium heat, add oil and onions. Sauté for 4 to 5 minutes, until onions are translucent. Add chopped rosa de Jamaica calyces and sauté for another 4 to 5 minutes, until onions and calyces are wilted. Turn off heat, add salt and remove filling from the pan. Wipe it out.
To build the quesadillas, start with one tortilla as the base, add a layer of shredded cheese, about 2 to 3 tablespoons of Jamaica filling, another layer of cheese and the second tortilla. Repeat with remaining tortillas.
Heat the skillet over medium high heat. Add quesadillas 2 to 3 (or as many as you can fit in your pan) at a time. Cook for 3 to 4 minutes on each side, pressing down on them to help mesh cheese and filling. Keep warm until ready to serve.