Before the flying type lover prompts the dialogue of asking you to show him how to train a pidgey, I believe you'll need to have caught data (doesn't need to be your OT) of all the flying type pokemon in kanto, excluding the legendary birds.
They asked to look at my pokedex and kept nitpicking that I didn't have caught data of pokemon with a flying typing (charizard, dodrio, etc.) and if I "really loved flying types" I needed to show that. After I got caught data on all the pokemon in kanto that had a flying typing and showed my pokedex to him, he stopped nitpicking about it then asked me the question about training a pidgey.
I still had missing flying type entries for other regions excluding kanto when he stopped nitpicking about it, so I believe it just stops there in terms of how many entries you need to have caught data on.