I had/have this same issue. When my iphone was full and ran out of space I ended up going into settings and deleting all of my music. When i did that, it kept the playlists and songs int the "Music" app but had no link to the actual songs on my phone because i deleted them. So whenever i would try to play a song it whould try to play one that i nolonger had on my phone and just keep retrying and got stuck in an infinite loop and thats why i saw the flickering play button.
not sure of the full solution but i know thats the cause. Tonight i am going to try to plug my phone in through itunes and remove broken songs that way