Are all the flies in the house dying suddenly a sign or omen of any kind?

Not all naturally occurring phenomenon can or should be interpreted as omens.

In this case I'm inclined to think you are observing a yearly event. As the weather gets colder, flies tend to try to find a way to stay warm. If they get indoors they can go dormant over the winter, appearing dead. Or they may die of natural causes, their life cycle is no where near as long as ours. The other possibility is that there is an insecticide at work here, people often forget they have put up things like "no-pest-strips' and then are surprised at the number of little bodies that appear on Windowsills etc.