Slack attained admission to the bar in 1892, and began to practice, first in Barre, and then in St. Johnsbury.[4] While in St. Johsbury, he first practiced as the partner of Alexander Dunnett.[5]
In 1910, Slack won election as Lieutenant Governor. He served in this position from 1910 to 1912.[7][8][9][10]
In 1913, Slack was appointed a judge of the Vermont Superior Court. He served until being named an associate justice of the Supreme Court in 1914. In January 1915, public outcry over the Vermont General Assembly's failure to reappoint longtime justices Loveland Munson and Seneca Haselton led to resignations and new appointments which returned Munson and Haselton to the bench. As part of this effort, Slack agreed to return to service as a superior court judge.
In 1919, Slack was again appointed an associate justice of the Vermont Supreme Court, and he relocated to Montpelier. Slack served on the court until his death.[11][12][13]
During World War I Slack served as Chairman of Vermont's Committee on Public Safety, a board convened by the Governor to mobilize Vermont citizens and materiel for the war effort.[14][15][16]