The method I devised to get rid of these large black flies from indoors:
Open a door and simply herd/walk them out by making yourself big. It's surprisingly easy - so much easier than trying to swat them. They seem to instinctively avoid things moving towards them, and because of that they're pretty easy to herd.
Relatedly - if you need to get a light-seeking insect (such as a moth) out of a room, you can just turn off all the lights and open the window. In general, people look at you like a wizard when you exploit the behavior of a creepy-crawly to get it to do what you want. For example you can catch a spider quite easily by placing a drinking glass in front of it and nudging its behind. It will panic-run forward into the glass.
The method I devised to get rid of these large black flies from indoors:
Open a door and simply herd/walk them out by making yourself big. It's surprisingly easy - so much easier than trying to swat them. They seem to instinctively avoid things moving towards them, and because of that they're pretty easy to herd.