You do get to tell us how your premise works, of course... but chickens fly just fine. Modern breeds are heavier (more meat), and being heavy they have trouble with sustained flight. They'll never fly 5000 miles south for winter, but to get to a low roost above where predators will get them is pretty doable for all but the heaviest.
Turkeys, too. Ducks. Geese. Most of the fowl that we eat, all of them gone.
Thus, no more chicken tendies... for anyone.
If that weren't bad enough, we have some birds who are competent pollinators of exotic plants. Hummingbirds mostly, but others as well. Some of those plant species are already endangered, so you're looking at a minor extinction event beyond just the birds themselves.
Other ecosystems rely on birds for food... reptiles a bit. Those populations if already endangered, could easily be pushed over the edge. Snakes, lizards, alligators and crocodiles maybe.
The good news is that this isn't without its benefits. So-called "bird flu" will be a thing of the past. The flu, as you all are no doubt aware, is a virus that likes to jump species. In particular, it will favor pigs and birds as well as ourselves... and birds being highly mobile are very good vectors. It's not as if one farmer's pigs are visiting the other farmer's pigs 10 miles down the road late at night. But birds will easily cover that distance in minutes, and may do so every day. They'll poop in the pig pens, pick it over for food, and then move on to the next. And then go poop on your car door handle. (Feces aren't a particularly viable mechanism, just one chosen to illustrate things in general.)
With those birds gone, it's quite possible that the flu will become less adaptive and widespread. It's possible flu epidemics would become a thing of the past entirely (though there's little hope for it becoming extinct itself).
Longer term though, there are other problems. Some of the richest phosphate deposits are from birds (bird poop again, I keep circling back to it). These things take tens of thousands of years to develop, but when ocean birds nest on certain islands generation after generation, their feeding on fish but pooping on shore in places where it doesn't wash away quickly tends to concentrate good old phosphorous there. That will cease. This won't become a problem for a long time, if ever, but it does demonstrate how many cycles and systems are being affected by their absence.
Similarly, birds have alot to do with how new islands are colonized at sea. Some seeds and animals can be washed ashore aboard detritus, but birds tend to carry alot with them as well. And not just islands, new lakes may actually be seeded by birds, who carry fish eggs with them in their guts, or snails on their feet.
If evolution ever replaces birds with something else (it's not guaranteed, some niches are difficult to learn to exploit), it will be many millions of years before that organism takes over the skies again.
We aren't in any immediate danger of becoming extinct in this world, or even becoming involuntary vegetarians. But the loss of the turducken as the pinnacle of culinary art will be grieved for all eternity.