my neighbors just got chickens and the fence is chain link separating the yards. should I be concerned of their new chickens spreading anything to mine? because I no longer can allow them to free range my backyard now.
Their chickens are in danger of catching something from yours as much as yours are from catching something from theirs, even more if theirs are chicks from a hatchery. Chicks from a hatchery are usually really safe.
Many flocks have what are called flock immunities. They have diseases or especially parasites that they have developed an immunity to but can give to other non-immune chickens. Yours could have one of those but because they are immune they don't show any symptoms. That other flock could have something too.
That fence won't help much as far as diseases and parasites. It will help keep the flocks separated. Chickens can change flocks on their own if they decide to. Some diseases and parasites are spread by direct contact, like eating or drinking out of the same dishes. But some can be spread by droppings. Say a chicken poops near the fence and it gets scratched to the other side. Sometimes critters are vectors. Mosquitoes, grasshoppers, or other critters can spread them. Some can spread on the wind from a flock a mile away.
A lot of people are in situations similar to yours and never have problems. I'm not saying you are at zero risk, you are not. Things happen. I can see a few options:
1. Keep as you are and maintain a good fence between neighbors. Watch for problems and react if you see something.
2. Isolate your chickens as far from theirs as you can.
3. Get rid of your chickens.
Good luck!