Add all the ingredients for the shredded chicken to a slow cooker and give it a good stir. The quantity of water you add will depend on the size of your slow cooker, but it needs to cover the bottom and come up the sides by about 3cm.
Turn your slow cooker on low for around 5 hours. Periodically (if you can) check to see if you need to add more liquid, but you shouldn't need to.
With half an hour's cooking time left to go, if the mixture is still quite thin you can add a cornflour slurry (1 tbsp cornflour mixed with a little water) to the slow cooker to thicken it up.
Once your chicken is cooked and shredding easily, you can store it in the fridge until you are ready to make your quesadillas. To do this, add 1/4 of the chicken, 40g black beans, 1/4 cup cheese and any veggies you'd like to your low FODMAP wrap or tortilla, and wrap it up. You can then toast it in a sandwich press or a pan.