Hlynka was known for calling for the liberalization of immigration policy to help bring displaced persons to Canada and for assisting in the immigration of Ukrainian displaced persons in the aftermath of World War II. He traveled to Europe after the end of the war in 1945, and undertook a fact-finding tour of the camps operated by the United Nations Relief and Rehabilitation Administration (UNRRA). He then played a leading role in the public campaign for immigration law reform, which culminated in Prime Minister William Lyon Mackenzie King's decision in 1947 to open Canada's borders to able-bodied displaced persons from Europe. It is believed that Canada accepted more than 34,000 Ukrainian displaced persons and refugees between 1947 and 1952.