Thawing and re-freezing chicken is no problem whether it was cooked or not. This is my experience, not the 1000 times safety factor of the FDA, which to me is way over the top. I was a credentialed National Sanitation Foundation listed employee at a facility that made commercial kitchen equipment, I have had to study about where germs live. If everyone followed the paranoid guidelines set forth by government and many web sites, which assumes everyone is an idiot and haven't stored stuff at the proper temps, etc., we would be throwing away a lot of safely edible food. And a lot of people do...I've seen someone pour out milk because the use by date had passed, without even sniffing it first. My mom will throw out leftovers past two days, while my wife and I will eat week-old leftovers without flinching, and have never gotten sick. The advice given by government and other places online and in books is to make sure you cant sue them somehow. Before refrigeration, families would get up and eat the leftovers from dinner the night before, for breakfast. Fully cooked, but not refrigerated. Often reheated, which kills bacteria.
People are paranoid about food storage. And if they are ignorant, maybe they should be. These are often the people who dont realize cross-contamination is what gets most people sick. That's when you let your fresh salad ingredients, for instance, come in contact with a surface your raw chicken touched that had not been sanitized. I may be fearless about fully cooked leftovers in the fridge, but I am fastidious about keeping raw meat, especially chicken away from other foods during preparation of meals. I clean my work surface well after handling raw meats.
The way you describe your question, it reads like you are making quesadillas in their complete form. That means you have fried/dry-fried the filling sandwiched between two, usually flour tortillas. You can safely freeze and reheat them, but the texture of the tortillas after that may not be great because the moisture of the filling will have leeched in to the tortillas.
Calling them "quesadillas" means the whole thing, tortillas and all. But if you are only referring to the filling (chicken cooked with other stuff), freezing then thawing and reheating-proceeding with the rest of the quesadilla cooking will work well.
You say when you buy chicken like this, you plan to eat chicken for three days. Your quesadilla filling would be fine just refrigerated for three days or more...in my experience...and I've lived to tell about it without gut problems for decades. In fact, your thawed raw chicken will be fine for at least two days...or more. Your nose will tell you if there is something wrong, and even if its slightly funky to the smell, fully cooking meat will kill most bacteria that will make you sick. For chicken thats about 165 degrees. If the chicken is cut off the bone and in to pieces, this temp is reached easily, usually.
