How do you get the Season 2022 - Flex Platinum Icon?
It was a ranked reward. Riot's description in the client reads: “This icon was earned by finishing Platinum in Flex Queue in Season 2022.”
Is the Season 2022 - Flex Platinum Icon still available?
No. The Season 2022 - Flex Platinum Icon was a ranked reward. To earn it, you had to reach Platinum in Flex during Season 12 (2022). Riot does not hand out past ranked rewards again, so you cannot earn this icon anymore.
