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?