Are you certain that these are common house flies, rather than drain flies? All of the suggestions so far, are for the former, and won't work for the latter. Drain flies look like smallish house flies, and breed in drains. they breed in the water in the trap. If you want to get rid of them, you have to attack the source. Get Rid of Drain Flies
We were parked next to a barn with farm animals. Flies Everywhere. We wanted to clear out the flies from the trailer while moving to next stop.
Deryl found a fly strip like thing at Walmart and hung it in the middle of the kitchen. It got all but 1 and we still haven’t got that one dead yet !
Some years, the flies are worse than others. You can bring an eco-friendly fly spray, burn citronella candles or citronella spirals. You can make your own spray with citronella, eucalyptus, clove, cedar, lavender, and peppermint essential oils in vodka or witch hazel (30-50 drops of any combo of these oils in a dark colored spray bottle). Peppermint, citronella, lavender and eucalyptus are fairly effective, but the more you have in the mix, the better. Spray everything including your table with the mix. It will keep away spiders and mosquitoes too.
Try hanging water balloons over your head. I went into a campground office once and the door was propped open with a big rock. There was an older lady behind the counter who was very nice and very talkative. She had a fly swatter in her hand and was swatting flies. There were two rather large water balloons hanging over her head. After we did our business we chatted for a while. As we talked she would swat, swat, swat and say "Damned flies!" As I was ready to leave I said. By the way, what are those water balloons for?" She looked at me like I came from another planet and said "They keep the damned flies away honey!" Could have fooled me!