"Flew The Coop" is an orchestral piece from the Season 6 soundtrack.
Locke tells Jack that a plane he piloted crashed, paralyzing him and leaving his father catatonic. Jack recalls the conversation they had at the airport and tells him that he must let go of his guilt and come to terms with the death that occurred. Jack himself has trouble letting go, but Locke's taking the first step could help them both.
Locke considers this for a bit then laughs and leaves. As he rolls away though, Jack says "I wish you believed me", and the words seem to recall something for him.
The piece is a variation on Locke's flash sideways theme.
"Flew the coop" usually means "fled to avoid arrest". Locke's story tells of his accident while flying his father, Anthony Cooper.