Finley was born and raised in Bernice, Louisiana. At 11 years old he began practicing the guitar he had purchased from a thrift store. Gospel music played a crucial role in his early development: "I always went to gospel quartet groups and I always took the front row seat, and I just watched their fingers", recollected Finley in an interview. In 1970, he joined the army, originally to serve as a helicopter technician in Germany. Upon his arrival, however, Finley accommodated the army band's need for a Guitarist and bandleader by traveling with the group throughout Europe until he was discharged.

After returning to Louisiana, Finley worked as a part-time street performer, leader of the gospel group Brother Finley and the Gospel Sisters, and as a carpenter. In 2015, Music Maker, a non-profit organization that supports aging blues Musicians, discovered Finley busking before a gig in Arkansas. He was deemed legally blind and forced to retire from carpentry. With their help, Finley made a musical comeback, featuring him in packaged tours with acts like Robert Lee Coleman and Alabama Slim.

Finley released his debut studio album, Age Don't Mean a Thing, on September 30, 2016 on Big Legal Mess Records. Although for the most part Finley was a bluesman, his record Producer Bruce Watson keyed in on more of his soulful compositions. With production credits from Watson and Jimbo Mathus, Finley traveled to Memphis to record the album with members of the Bo-Keys. He penned all but two of the tracks, highlighted by an autobiographical title song, on Age Don't Mean a Thing, evoking influences from Booker T. and the MGs, James Brown, and B. B. King. Music journalists were highly receptive to Finley's comeback and album, particularly his revitalizing take on Southern soul.

After Age Don't Mean a Thing, Finley got connected with Dan Auerbach of the Black Keys. Auerbach and Finley then released an original Soundtrack for the graphic novel Murder Ballads published by z2 Comics. Shortly after the release of the Murder Ballads Soundtrack Billboard announced that Finley would be releasing a full-length album produced and co-written by Auerbach. The album, GOIN' PLATINUM! was released on Easy Eye Sound (Nonesuch Records) December 8, 2017. The following year Finley joined Auerbach's Easy Eye Sound Revue tour.