Flinn made his Major League debut during the 1978 season, eventually appearing in 13 games while pitching to a record of 1-1 with a bloated 8.04 earned run average over 15.2 innings.
The following season he’d only appear in four games for the eventual American League champs, not factoring in a decision while not allowing an earned run in 2.2 innings.
1980 would see him suit up for the Milwaukee Brewers where he appeared in 20 games, going 2-1 with an ERA of 3.89 along with two saves in 37 innings of work, but it wasn’t enough for him to stay up in the Big Leagues, as he’d spend all of 1981 in the Minors before making it back in 1982 with the A.L. Champs for what would end up being the last five appearances of his career, this time back in Baltimore, when he went 2-0 with a very nice 1.32 ERA over 13.2 innings pitched.
After a couple of more years down in the Minors for the Baltimore organization, Flinn retired after the 1985 season, leaving the game with a record of 5-2, posting an ERA of 4.17 over 42 appearances and 69 innings pitched.
