[citation needed] Universal health care, which had been proposed formally by the St. Laurent government at the 1955 federal-provincial summit on taxation, would become his nemesis because of his reluctance to sink the budget of the province.
He sought a seat in a by-election in southern New Brunswick in 1960 and was re-elected to his home district four times before he retired from the House of Commons of Canada in 1972.
His grandson Ted Flemming was elected to the provincial legislature in the 2012 Rothesay by-election and served as New Brunswick's minister of health from 2012 to 2014.
Flemming's family-run lumber mill in the village of Juniper, New Brunswick ran into financial difficulties in the late 1970s, but his friend Harrison McCain, organized an investment campaign that raised sufficient capital from businessmen to allow the mill to make a financial recovery.
[3] The Hugh John Flemming Forestry Centre in Fredericton is home to the Maritime College of Forest Technology as well as several branches of the governments of New Brunswick and Canada, and the K.C.