The reason you have a cough is because toxins are being released/detoxed via the lungs. There is a few ways the body detoxes toxins, one is via the skin (sweat), the second is via the bowels (going to the bathroom), and the third is the lungs. The lungs are the dumping grounds of the body, so if you are killing candida, the toxins will be released via the lungs.
When I started out on the diet, I had a pretty bad cough with lots of mucous and I basically had flu-like symptoms. These are all die off symptoms and almost everyone should experience a cough due to die-off. For me it lasted a few weeks to a month or so and then went away. I still get maybe one cough a day (I’m a smoker) but not like it was during he die-off period.