Let's say I have a few chickens in my backyard that don't have bird flu, and we (myself or my chickens) never come into contact with any other chickens.

Aren't we safe? If not, what are the possible vectors? Is it from random birds flying in my yard? My visits to grocery stores?

No, you're not safe if your chickens are exposed to wild birds. If they're outside feeding on seed that other wild birds also have access to they're at risk.

Other comments mentioned wild birds, but lots of animals can spread bird flu. House cats, for example.

Edit: link (gift NYT link) https://www.nytimes.com/2025/02/06/health/cdc-bird-flu-cats-...

The chickens can get sick from bird droppings, from birds that fly over your chicken run and never even come into direct contact with the flock.

Your birds could get sick from other birds. It doesn't just affect chickens. I'd exercise precautions with your birds. Both to keep them quarantined from wild birds and keep yourself and family quarantined.