I don't know, they run after me when I run on my lawn with food in my hands ;) Or even just a Tupperware for that matter (empty, going to fill with veggies from the garden).
I was thinking a bird like a pheasant would enjoy flying, no? There must be at least one backyard bird that likes to fly and would appreciate a little exercise, just like our dogs do. I thought that would be the first motivation, and secondly the desire to stay with the "flock"? If that bird was taken as a baby and cared for and neutered by a human, wouldn't it want to follow the human?
The reason I first thought it could be possible is because I thought of Bill Lishman, the man who flew a little glider and was able to lead a pack of goose to migrate. He used a different path that what the goose would usually use and they followed. He was really part of the flock and they flew everywhere with him. He is even re-introducing some extinct birds to North America by flight!
And this french guy did something similar. At the beginning of the video his "aircraft" is still on the ground, taking up speed for take off, and the bird fly beside him. That is the closest I could find about the fact that running with birds might be possible ;).
I am almost certain my rooster would fly with me if he could. He was attacked when he was 5-6 weeks old and I took care of him. Since then he comes in the house (asks the door like a dog, comes in and out), sleeps with me when I watch TV, follows me around.. but I think he is blind in one eye, plus he is a meat bird, so I've never even seen him take off the ground. Not sure he can. But if I had saved a laying hen as example, that would be fit and slimmer than him, I bet she would follow me! Ok, not far, being a chicken.. but still ;)