Hello
Our staff are on holiday break until after New Year’s Day. I can give you some information on indoor flies that may help.
This may be a cluster fly. If you capture a few and freeze them, you can examine them closely with a hand magnifying lens and compare to the pictures here, note the different colors of hairs, eyes, etc. when trying to identify which you have- 
https://extension.entm.purdue.edu/publications/E-7/E-7.html

The bulletin suggest insecticides that you can safely use. If you used them be sure they are labeled for indoor use, and please follow all directions and precautions. Sticky fly traps may be useful, too.

I will send this along to one of our entomologists. His response may be delayed until after the holiday break. Thank you for your patience.

This sounds like it is probably cluster flies (Pollenia rudis). They enter homes in the fall through cracks and crevices or other openings in the exterior for the structure. They are not harmful; they do not reproduce indoors or feed on anything inside of the structure. This is just a normal part of their overwintering behavior. You can prevent them from entering the structure by working hard to seal up cracks in the exterior. Especially, around doors and windows or vents that penetrate the exterior of the home. Ensuring that weather seals are in good condition and that all openings are sealed or have screens installed, will reduce the numbers of flies that gain entry to the interior. Once they are in the home, using a vacuum cleaner to suck them up, is a good option. Insecticides are costly and may not have a great impact on the number of flies you see inside of the home. 
You can read more about cluster flies and management options in this article from MSU Extension:
https://www.canr.msu.edu/resources/cluster-fly