My husband is just getting over the flu and said that he had a dark green stool with mucus. Would that have anything to do with the flu?

Maybe. Sounds like bile... If he's been unwell he may have (temporarily) lost the enzymes that live in the small intestine - this leads to a temporary lack of digestion. It will get better. Likely avoid dairy for a week or so and see how it goes.
Depends. Influenza is a fairly acute illness most commonly in the colder months of the year with chills, fever, respiratory symptoms, and occasionally abdominal symptoms. Viral gastrointestinal illnesses are due to different types of non respiratory viruses and are associated with vomiting and diarrhea.. Green stool with mucus can occur with either illness .Report to md if severe or persistent.