A deer fly goes after movement and the color blue, so your traps tend to be sticky traps, like a lowes bucket coated in tanglefoot. but you can't feed them to fish, chickens and they're a pain to clean.
I've been looking for someone to scale up some kind of fan trap for deer flies, like think a bigger version of the Katchy UV traps, but so far nobody has done anything. A fellow had a good example of using blue nitrile gloves blown up and coated in tanglefoot on a stick but while cheap, still messy.
Do that, but paint the fan (with blades) blue. If more movement is needed, you could probably do something pretty simple with a plastic plate painted blue and hung about a foot from the fan intake.
Cleanup isn't great, but it's better than sticky traps. Spray the mesh down with a 50:50 water:alcohol solution as needed to kill live flies in the trap before dumping.