Seattle received a second-round pick in 2022, a third in 2023 and a seventh in 2024. The second-round pick this summer is the one the Flames previously acquired from the Florida Panthers.
The Kraken are retaining half of Jarnkrok's $2 million salary cap hit for the rest of the season.
Jarnkrok, a 30-year-old Swede with 26 points in 49 games this season, boosts Calgary's chances to make an extended postseason run through the Western Conference. The Flames earlier this season acquired forward Tyler Toffoli from the Montreal Canadiens.
"I want to thank Calle for everything he did for the Seattle Kraken, and we wish him all the best in Calgary," Kraken general manager Ron Francis said.
Giordano was held out of the lineup for the Kraken's game Wednesday night against Tampa Bay to prevent him from getting injured. Giordano is a former captain of the Flames, and there has been buzz of Calgary making a run to reacquire him.
Jarnkrok is another of Seattle's expansion picks that will not finish its inaugural season with the Kraken. Earlier in the season, the club placed forward Nathan Bastian on waivers, and he was quickly picked up by the team that lost him in the expansion draft, the New Jersey Devils.
The Associated Press contributed to this report.