Vlam joined the Church with his mother and siblings when he was 16. In 1914 Vlam joined the Dutch navy. In 1929 he married fellow Church member Hanna, who was a native of Switzerland. They had met while Vlam was supervising diesel engine constuction for the Dutch Government. At this time Vlam was serving as president of the branch in Winterthur. Vlam had previously also served for a time as branch president in his native Den Helder. In 1933 he was stationed in Surabay, Indonesia. In 1939, on his return to the Netherlands, the family traveled through Salt Lake City and there Pieter and Hanna were sealed to their children Grace, Heber (named for President Heber J. Grant), Vera, and Alvin.
When foriegn missionaries were withdrawn from the Netherlands on the eve of World War II, President Joseph Fielding Smith, who was conducting a tour of the missions in Europe, called Brother Vlam to serve as the second counselor in the Netherlands Mission Presidency.
Brother Vlam was, in May 1942, taken as a prisoner of war along with the rest of the Dutch Military. He was imprisoned at Stalag 135. While in the prison camp, Vlam taught many people the gospel. Among those he taught who joined the Church after the camp was liberated was J. Paul Jongkees, who would later serve as the first Stake President in the Netherlands.
In 1949 the Vlam family moved to Salt Lake City to be with the body of the Saints, and where they could go to the temple often.