My take is that the voice in his head and the flying were meant to be a representation of how he viewed his career and his self throughout his early life. The voice is when he was at his peak POPULARITY....the Birdman...so that is his voice. His ability to move things around was just an extended representation of that....how he saw himself and how everyone else saw him for a brief time in the past....but doesn't see himself that way now.
But...he is making this play and putting his money on the line because he has finally realized he traded a relationship with his daughter and his wife for that "ability", and it is his last ditch effort to make his legacy match the voice in his head and the "powers". He thinks he messed it up with his daughter, but hopes to at least become something she can be proud of from a career/legacy standpoint.
She, in the movie, cared more about the relationship than his career....but it shifts as they bond a little over the social media thing. She even makes his twitter page and that speech telling him he can have "power" and that she gets it and he doesn't. By the end she starts seeing him a little differently, and I think the ending is simply meant to represent that finally....at the end.....SHE saw him more at that figure he was seeing all those years.
The taxi scene gives away....very cleverly...that it was something he was seeing.....that he is the ONLY one who sees himself that way or wants to.
At the end, the only other person who saw him that way too was his daughter.....he was flying again and they had reconnected a little.
That is what I got from it anyway.
It worked for me. I never really embraced the idea it was supposed to be "real"
And I also think it was meant to translate to regular life, not just "celebrity". A lot of people have that way they see themselves, then the way your family sees you, and maybe the way you really are.....even if you are a Shoe Salesman (tm Al Bundy).