How do you get the Season 2020 - Flex Challenger Icon?
It was a ranked reward. Riot's description in the client reads: “This icon was earned by finishing Challenger in Flex Queue in Season 2020”
Is the Season 2020 - Flex Challenger Icon still available?
No. The Season 2020 - Flex Challenger Icon was a ranked reward: to get it you had to reach Challenger in Flex during Season 10 (2020). Riot does not give out past ranked rewards again, so it cannot be earned anymore.
Season 2020 - Flex Challenger Icon is one of the rarest LoL summoner icons.
