2010-11: Haydn Fleury appeared in three games with the Notre Dame Argos midget AAA team and skated for the Notre Dame Hounds bantam AAA team in Saskatchewan. The Regina native had one assist in three midget games. In 21 games for the Hounds he scored 7 goals with 19 assists and had 30 penalty minutes. Fleury was selected by Red Deer in the second round (43rd overall) of the 2011 WHL Bantam Draft.
2011-12: Fleury made his WHL debut — appearing in four games with Red Deer — skating most of the year in Saskatchewan midget hockey with the Notre Dame Argos AAA team. He also played for Team Saskatchewan in the 2011 Western Canada U16 Challenge Cup. Fleury had no points more penalty minutes and was +1 with Red Deer. He scored 6 goals with 15 assists and had 60 penalty minutes in 39 regular season games for the Argos. In eight playoff games he scored 1 goal with 4 assists and had 8 penalty minutes.
2012-13: Fleury skated in 66 of 72 games for Red Deer in his first full WHL season and played for Canada Western in the 2013 U17 World Hockey Challenge. The third-leading scorer amongst Rebels' defensemen, he scored 4 goals with 15 assists and was +4 with 21 penalty minutes. Red Deer finished third in the Central Division and reached the second round in the playoffs. Fleury had 2 assists and was +4 with 4 penalty minutes in nine playoff games.
2013-14:Fleury played for the gold medal-winning Canada U18 team at the 2013 Ivan Hlinka Memorial Tournament in August before returning to Red Deer for his second season. Named an assistant captain for the Rebels.