Stage one: the hens settle before anyone meets them
Give the new flock at least a week or two in their coop and run before any introductions, so they learn where home is, where the roost is, and come to the run's fence confidently at the sight of you and the feed scoop. Hens that know their ground bolt somewhere sensible when startled; hens that arrived yesterday scatter. During this stage the dogs will discover them through the fence, which is exactly what you want — the first many encounters should happen with wire between the species and nothing at stake. Start rewarding the dog for noticing the hens and then looking back at you, so calm disinterest gets established as the household rule before freedom enters the picture.
Teaching the dog what the hens mean
Build the dog's behaviour away from the hens first: a reliable recall and a solid leave-it, practised in the garden at a distance where the dog can still think, earn heavy rewards. Then work on a long lead at whatever distance keeps the dog able to respond — for many dogs that starts across the garden — walking, settling and playing while hens scratch in their run. Shrink the distance over days and weeks, never faster than the dog's calm allows. The red flags are fixation: hard staring, stalking posture, whining or lunging. A dog showing those goes back a stage, not closer, and a single unsupervised chase can undo weeks and can kill a hen even without contact, through shock.
First free meetings, and the cat question
When the dog is genuinely bored by hens behind wire and responsive on the lead beside the run, start short supervised sessions with the hens ranging and the dog on the lead in the garden, at a quiet time of day, and end while everyone is still relaxed. Only a dog who has stayed loose and responsive through several of those earns off-lead time, and even then, supervision stays until the pattern has held for weeks. Cats are usually the smaller worry with adult hens: a full-grown hen is big, confident and armed with a beak, and most cats learn to give the flock a wide berth after one inspection. Chicks, pullets and bantams are a different matter and need cat-proof housing and runs until they are fully grown.
Housing and habits that keep the peace permanent
Whatever the daytime harmony, the coop closes securely every night — foxes do not respect introductions — and hens always need escape architecture in the garden: shrubs, low branches, a table or ark they can duck under if a dog gets bouncy. Keep feeding the hens in their run rather than scattering food across the garden, so the dog never learns that hens predict scattered treats worth competing for. New birds joining later go through the same stages, not straight out. A mixed household works when every human applies the same rules. Through KinsLe Family Sharing, a grandparent or other relative you have picked can open the hens' profile directly.