I suspect Scott Walker is an INFP for several reasons.
He is incredibly shy and rarely gives interviews.
He is sensitive to criticism, although he doesn't let it affect him as much as he did in his younger years.
If you look at the history of his early solo albums, after Scott 4 (his best album, in my opinion) and Til The Band Comes In (meh) both flopped, he took it pretty hard and his creative side basically retreated. He recorded a string of uninspired albums that featured no original compositions, and it would be eight years until he recorded original songs again (Nite Flights, '78). That inability to cope with critics' and public's rejection of his art just screams INFP to me. I can totally relate. An ISFP (Bowie, for example) would've put any failure behind him and quickly moved on to his next project. An INFJ would not have taken the criticism as hard.
INFPs can also be notorious perfectionists. That could explain the massive amount of time between his last several albums (if you don't count musical scores and the occasional song appearing on a soundtrack): 11 years between Climate of Hunter and Tilt, another 11 years between Tilt and the Drift, and 7 years between The Drift and Bish Bosch.
Also, something about his lyrics seems very INFP-ish to me. There's a real childlike naivete, especially on his first four albums. At the same time, his lyrics can seem so wise and world-weary, like the musings of an idealistic bard.
He's probably also a type 4 enneagram.