Note: all I write is for my location, and I'm pretty lucky in regard of parasites here.
For the house fly and similiar types, reduce their breeding options. I have wooden hutches, and keeping those clean is not that easy, if poop accumulates long enough in a crevice or corner there will be fly eggs. Those flies are a nuicence, but mostly harmless.
Breeding spots for insect eating birds might help too. And trying to invite hunting insects like Asilidae, dragonflies, hornets, wasps etc. by tweaking the environment. For example, the jerusalem artishocks I planted around the hutches for shadow are a good hunting ground for Asilidae (actual picture from my garden).
Those natural methods will not completly rid you of flys, you just live with the good feeling that it would be worse otherwise, and you can enjoy the diversity
For the less harmless flies I made traps. A glass with a dark cover with a few holes (flower pot), and those holes shielded from direct light (random black plastic hot glued in place). Flies go in, but try to escape towards light, since the openings are darker than the glass they are trapped. Those traps attract those flies, so better put them somewhat away from where you don't want them.
As bait I put water and some pieces of meat or bones in it, very little is enough.
WARNING: Those traps are the most disgusting things I ever encountered, emptying them really brought me to my limits. But they work. Use the biggest glass jar you can get. And a gas mask for emtying :cheesysmile:
I also have heard of guinea fowl of being great at reducing insects, may be worth reading into that.
I use golden malrin fly poison, in a dish, on top of the metal roof over the hutches.[or under the hutches]
It is very toxic, and can also be used to kill any animal..so extreme care should be taken..
That is why I put it on the metal roof,or under the hutches.
If anything should spill it, it will not get in the rabbit feed, or in with the rabbits.