Brown signed for Dundee in July 1923, whilst travelling with the club on their Spanish tour. He had previously been with Newtongrange Star, in Edinburgh, for three seasons. Brought in to replace David Raitt, he soon settled into the team.
His first game for the club was in a friendly against Real Madrid, which Dundee won 2-0. But his first competitive match was on the 25th August 1923 in a 5-1 win home win against Hearts.
He was nominated as captain, in place of Colin McNab, for season 1930/31, with Alex Troup as his deputy.
An unfortunate incident happened in the home game against Aberdeen on 20th September 1930. Daniel McKenzie was injured after a tackle with Finlay midway through the first half, suffering an injury to his kidneys. He was carried off the pitch and examined by the doctor. Against the doctor’s advice he took to the field for the second half. Becoming seriously ill at the end of the game he was rushed to hospital, and had a kidney removed. Sadly a year later, McKenzie suffered a relapse from the injury which he didn’t recover from, dying at the age of 22.
Brown’s only international call up came in 1931, when he was selected for the Scottish League team, who were to play the Irish League at Windsor Park, Belfast. Scotland lost 3-2 in front of a crowd of 15,000 spectators.
After eleven years at Dens, and being a stalwart of the team, Finlay transferred to Darlington in March 1934. He had struggled with injuries the previous season, but had regained fitness after a successful cartilage operation. His last match was an away game against Aberdeen on January 2nd 1933, Dundee lost 3-2.
By August he was back at Dens Park. Not wishing to relocate down south, he returned to Dundee taking up the position of trainer of the reserve team. By 1936 he was assistant trainer to the first team alongside James Stewart. During this period he would also turnout as the “home linesman” at Dens Park.
When the club closed down at the start of WW2, Finlay, along with Andrew Cunningham (manager) and William Arbuckle (trainer) were released from their positions. Only the groundsman, David Hunter was retained.
He died at the age of 75, in Dundee in 1977.