A lot of the most common avian diseases and such don't really stay in the system all their life, like an STD. It's just most of them, if left untreated, will stay there and spread like wildfire through a flock. Chickens are pretty tough in that they can be sick weeks before you notice a problem. Which is why usually if the bird looks sickly, it's hard to save it by then, becuase it's already been so weakened.
The majority of the things we try to keep out of our flocks can be carried through droppings and water. So you do have to be a bit more careful with birds than other pets, because as I said before, they can carry things you aren't even aware of. The flock drinks from the same water, and the little guys poop 24/7, so having a 'closed flock' does help disease-wise. HOWEVER, if you don't want to inbreed, you can always bring in new blood and quarantine the new birds before introducing them to yours.
Of course wild birds are a huge part in spreading avian diseases, so unless you have the chickens locked in a solid building, you're never really completely 'safe'. But generally, free range chickens and such already have pretty good natural immunities built up from being around so many different species of birds, chickens, and other animals.
