I've been using Rescue brand non-toxic disposable house fly traps for years. They are incredibly effective. The flies simply drown in the water that you added when you hung it up. Hang one up; and, then 2-4 weeks later hang up another if and when it's too full to hold any more flies (or when the first one loses its punch). I like to keep two traps going side by side (one older; one new). I simply seal the oldest one to be discarded in a one gallon ziplock bag and put in trash (after draining liquid so that accidental seepage is avoided). [I drain it on the ground underneath where I hang them.]
Note: The odor that the bait uses to attract the flies is unpleasant, so hang downwind and at least 20 feet away from house. Since I compost all of our food scraps and grease using Black Soldier Fly larvae in my leaf composter, we don't have houseflies being attracted to our garbage can. But, if we did, I'd hang it there. Instead, I hang it at the other end of our yard closest to the problematic neighbor who raises chickens.