AIUI the Conspiracy Theory isn't that birds don't exist, but that they are not real. All the birds you've seen were actually government spy cameras.

This feels more plausible if you've only ever encountered pigeons and at some distance. If you've owned a parrot or some chickens, it is very apparent that this is not a spy camera. In fact the word I'd use for chickens is "saurian". They're clearly just lizards with feathers, if I didn't know their evolutionary story it would still scream at me when I see one laying on a rock in the sun that this is a lizard.