We have lots of wild birds. The only problem we've been able to identify and partially eliminate, over the past 10yrs, have been fowl mites in recently vacated wild bird nests (usually IDed on ground after strong winds). Only the roo was affected (was picking him up daily for treatment of bumble foot so infestation was eliminated - ivermectin - before it really started).
Keep feeders inside coop and a bit of netting over open door (pin up at corner so chooks can enter/exit but nasties, like European Starlings, have more of a problem doing so.
There's really no way to completely rule out transmission from these potential vectors of disease/vermin without an indoor aviary.
As was mentioned above, keep an eye out for dead wild birds but, more importantly, spend about 15min. minimum, a day, observing your flock. This allows for early intervention when changes that might indicate illness occur.