This gave them a direct spot into the final against Alberta's Colin Davison, to whom they lost 6–5 amidst a controversy involving a burnt rock.

Koe's early career included skipping Team Alberta at the 2000 Canadian Mixed Curling Championship, with teammates Susan O'Connor, Greg Northcott and Lawnie Goodfellow.

Up until 2010, Koe had little success in his attempts to win a provincial title on the men's stage, as he and his rink were in the shadows of fellow Edmontonian Kevin Martin, widely considered to be one of the best curlers of all time.

In both the 10th and 11th ends, his team's then-fourth player, Blake MacDonald (Koe skipped and threw third stones) had a draw to the eight-foot to win, but missed on both opportunities.

Two months after winning the Twin Anchors Invitational, the team played in the 2009 Canadian Olympic Curling Trials, finishing the round robin with a 4–3 record, missing the playoffs.

Later that season, Koe finally won a provincial championship, benefiting from an absent Martin who would be preparing for the 2010 Winter Olympics.

He was helped by the fact that the Olympic champion Kevin Martin rink lost in the semifinal, avoiding a final match-up of province's top two ranked teams.

The next month, Team Koe played in the 2013 Canadian Olympic Curling Trials, but finished with a 2–5 record, missing the playoffs.

With his new team, Koe successfully repeated as Albertan champion in the 2015 Boston Pizza Cup, which qualified him to represent Alberta at the 2015 Tim Hortons Brier.

On the tour, his new team won the Direct Horizontal Drilling Fall Classic and the Karuizawa International Curling Championship.

After going 8–3 at the 2016 Tim Hortons Brier, Koe and his foursome railed off three straight victories in the playoffs (again having to come out of the 3 vs. 4 game), defeating Newfoundland and Labrador's Brad Gushue in the final.

The team would represent Canada at the 2016 World Men's Curling Championship, losing just one game en route to winning the gold medal.

Koe again led his team to an 8–3 round robin record, and again had to fight through the 3 vs. 4 game and the semifinals in the playoffs to make it to the final, where he faced Brad Gushue in a re-match of the 2016 Brier.

[8] The team was devastated by the upset loss, with their head coach John Dunn telling CBC News a year later that "The Olympics will scar all of us who went through that forever.

"[9] On April 15, 2018, Koe won the Player's Championship Grand Slam of Curling event with a 6–2 victory over Niklas Edin of Sweden.

Koe and his new team began the 2018–19 season by winning the first leg of the Curling World Cup, defeating Norway's Steffen Walstad in the final.

[15] The win earned the team the right to represent Canada at the 2019 World Men's Curling Championship where they finished the round robin with a 9–3 record.

They then won two playoff games to qualify for the final where they lost to Sweden's Niklas Edin rink 7–2, settling for silver.

Despite the lack of any event wins, their strong play was good enough to award them with the Pinty's Cup for the season's best Slam team.

[19] Team Koe started their 2019–20 season at the 2019 AMJ Campbell Shorty Jenkins Classic and lost in the quarterfinal to Brad Jacobs.

At the 2019 Canada Cup, they finished the round robin with a 5–1 record, which qualified them directly for the final which they lost to the John Epping rink.

[22] At the 2020 Tim Hortons Brier, representing Team Canada, they finished the championship pool with a 7–4 record, which was in a four-way tie for fourth.

[29] Because Team Koe ranked 6th on the CTRS[30] and kept at least three of their four players together for the 2020–21 season, they got the second Wild Card spot at the 2021 Brier in Calgary, Alberta.

[33] The Koe rink won their first two events of the 2021–22 season, the ATB Okotoks Classic and the IG Wealth Management Western Showdown.

[40] It was later announced that Koe would skip a new team consisting of Tyler Tardi, Brad Thiessen and Karrick Martin for the 2022–23 season.

There, the team went 4–1 in pool play, and then won all three of their playoff games, including defeating Switzerland's Yannick Schwaller rink in the final.

However, the rink still participated in the 2024 Montana's Brier as the top non-qualified team on the 2023–24 CTRS standings following provincial and territorial playdowns.

[44] At the Brier, the Koe rink, who was at the time the third ranked team in the country, finished pool play with a 2–6 record, failing to qualify for the playoffs.

Koe called the feeling "about rock bottom" and blamed the team's failure on their draw weight during key moments.

Kevin's father, Fred, a politician and former skip, participated at the 1999 Canadian Mixed Curling Championship alongside Jamie and Kerry.