Best ways to control flies?

Other than running chickens a few days after ruminants in grazing pastures (a la Salatin), what have you all found to be effective ways to keep flies from becoming a nuisance while keeping sheep or cattle? The 3 lambs I had last year came with quite an abundance of flies that liked the invade the house.  Once the lambs were slaughtered the flies started to abate, but we had to put up fly strips they got so bad inside the house.  

Poultry?
Chickens are said to be good for eating fly larva out of cow pies and spreading the manure around.
Muscovy ducks are said to be active avid and excellent fly catchers.

Edit: clearly I did NOT read your question fully!
My apologies.

One non-poultry, toxic free  counter  to flys is a mesh trap baited with funky nastiness, such as a rotting piece of shrimp.

Here is a home made one :

https://www.instructables.com/id/Industrial-Fly-Trap/

I have heard, but cannot personally attest,  that moving your animals in rotational grazing paddocks will lesson flies and parasites. The animals have moved on before the 'bugs' hatch and this breaks the vector(animal) needed for the parasites life cycle.

I was rotating the lambs plenty often.  Had turkeys in the same general area.  But still had tons of flies in the house.  Might work better with chickens.  But still, the flies were pretty bad.

What timing!  Paul and I are working on the Animal Care badge for the PEP program and I was just looking into a list of things to do for flies.  Here's the list I found after a little searching.  Some are for inside, some for outside:

create dragonfly habitat
create frog habitat
create toad habitat
attract two different fly eating birds/bats
Remove fly specks (apparently they attract other flies with the specks they leave on the walls)
Eliminate breeding sources
Plants that deter flies (wormwood, mint, etc)
Fruit fly vinegar trap
Willow feeder style fly trap
Homemade fly paper (heated corn syrup and paper)
Carnivorous plants
Import beneficial nematodes
Clear bag of water hanging in a window (bizarre but apparently it messes with their eyes)
plants/habitat for predatory wasps

Many of these ideas came from https://www.fliesonly.com/how-to-get-rid-of-flies/

Subscribing to a fly predator service helps a lot ~ they mail a batch of eggs every month, you wait till they start hatching, then sprinkle them in areas of manure. I think they feed on the larvae in the manure. Those, plus traps for the flies that do hatch out, can put a real dent in the fly population. Once in the house, a round with a good swatter twice a day also keeps them in check.  Not sure how hard it is to breed ones own predators ~ I think the subscription runs around $20 per month for 8 - 10 months?

I'm a big fan of encouraging dragonflies. They make quick work of 'pest' bugs including flies once they get acclimated to your area. You need to encourage habitat formation and look into providing breeding grounds for the dragonflies but then they do the rest.

My chickens have, however, started getting pretty good at snatching dragonflies out of midair these days. Just something to be aware!

After getting my face butchered a year or two ago, I use lots of fly traps.

How about a few *actual* venus flytraps (or other carnivorous plants) as houseplants?  they'd need to get large enough to trap several flies per plant, but if your home environment is conducive to their survival year-round, that's an effective (and cool to watch) way to lessen the fly load.  Fun with flyswatters (contest for who gets the most, or the highest percentage of successful swats) especially at the dining table; pointing a fly out to your cat to chase (in a room without lots of breakables or plants to damage;) or as a last resort, flypaper.    

Despite having horses next door and cattle across the street, plus our own chickens, turkeys, and dogs who do their business outside, this year we've had practically no flies get into the house.  We try hard not to keep doors open any longer than absolutely necessary, otherwise the only difference is that my elderly mom who used a walker (and took lots of time to get through a doorway) is no longer here.  Oh, and we adopted a few more cats who like to chase bugs!

How timely!  Thanks.

Currently I have an abundance of flies.  The way the house was constructed they can come through the walls.

In the house, I do the fly swatter thing throughout the day.  They gather mostly in the kitchen, and I have a couple swatters at the ready.  I swat them when I see them.  They gather around dead flies if I leave them, and around bread crumbs, and spilled milk and so forth.

The best time for killing flies is at night. The majority of them go to sleep on the ceiling. It is easy to swat them or if you get a jar of water and put some foaming soap or detergent in there, then you can raise the jar up underneath the fly and when the fly tries to fly away, he has to let go of the ceiling and does an inch or two of freefall, and falls into the soapsuds and cannot get away!

Outdoors, I make a fly spray for the walls of the milking parlor. It is white vinegar, clove, and bay leaves and water. It doesn’t last a long time, but it does deter the flies from landing on the goats and the walls.

None of these is working well enough to suit me!  Good to know about the dragon flies and muscovy ducks, as I am in the establishing systems phase.

Breeding habitat for dragonflies is what?  A pond or a creek?  If a pond is what they need, what’s mosquito prevention?

(if it’s a simple answer great. But if there’s already a discussion or there is going to be a lively discussion about the mosquito prevention going off topic, then can someone please put a link here to the existing or soon to be existing thread. Thank you).

Thekla McDaniels wrote:
...Good to know about the dragon flies and muscovy ducks, as I am in the establishing systems phase.

Breeding habitat for dragonflies is what?  A pond or a creek?  If a pond is what they need, what’s mosquito prevention?...

I can't really answer your questions except to say: 1. We encourage dragonflies to eat mosquito larvae so there ya go. 2. I did not realize they eat flies too.

I saw a provocative video (some gardener) showing that high poles and wire give dragonflies somewhere to sit and watch for other bugs to eat. I have only put up a few in the backyard, which is where we have a skeeter annoyance, and definitely see them sitting on them, but now I'll want to multiply and also extend elsewhere.

Also looking forward to the breeding habitat answers!

PS Pretty sure this is the video I saw before, at any rate same system:

Arbico Organics has a solar fly trap that is $90 or so but is reusable year to year. I have tried the fly larvae eater but it is hard to keep up with. The solar fly catcher uses a yeast bait with whipped egg and carbonated beverage. All non toxic. It works and will buy a second next year.
Also I take the pop up reusable fly trap and mix  an egg , two tablespoons of proven yeast, carbonated beverage and one of their baits and make a gallon which I add a little to the trap once a day. Anything that stinks like old milk etc brings them in

I had tons of dragonflies when I had several acres of fields that were allowed to grow wildflowers and whatever else wanted to grow there, including multiflora rose.  There was always something or other blooming, there were plenty of natural high perches, and I assume multitudes of insects for them to eat.  But like the guy in the video above said, the dragonflies don't come out until the insect populations have had a chance to increase enough to feed them.  It is the end of July, and I only recently began seeing them here in our butterfly/hummingbird garden, several weeks after the lightning bugs came out.  

We have gambusia fish in our small pond for mosquito control. They are small like minnows and easy to keep. The pond attracts lots of dragonflies but they don't seem to make a dent in the fly population!