Fluke affects certain parts of the country more - caused by snails, I think. There would be other symtoms besides a cough, such as lethargic, poor condition, not eating etc. Sheep seem more prone to it. I can't see your goat having that, but I think the vet can test for it if need be.
It affects the liver.
I have never seen a goat with it, but yes, they can get it. I would not worry about that being the cause of the cough though.