A career minor-leaguer, Allen began playing hockey out west in numerous small towns, from North Battleford to Lethbridge to Creighton during the mid-1930s.
Allen signed with the New York Americans on October 15, 1940. He would appear in six NHL games for the club, but suffered an eye injury in the final game and was returned to the AHL upon his recovery.
The following year Allen was traded to the Pittsburgh Hornets, the AHL affiliate of the Toronto Maple Leafs, with Glenn Brydson in exchange for Phil McAtee and Peanuts O'Flaherty. Allen would score 20 goals for the Hornet in just 51 games during the 1941-42 season.
Allen spent much of the next decade in small American cities playing in far away leagues that would never see him promoted back to the NHL, finishing his tour of duty first with the Dallas Texans and then with the Saskatoon Quakers in 1950.
A speedy right winger, Allen had shown an ability to score, most notably with Pittsburgh in the AHL where he had 20 goals in 1941-42, his first full year after the injury. Later, with the Texans, he led the league with 34 goals in 1946-47 and two years later he suffered a leg injury which eventually led to his retirement, in 1949, at 33 years of age.
In 1995 Vivan "Squee" Allen passed away and was later buried in Kerrobert, Saskatchewan.