How do you get the Season 2015 - 3v3 Platinum?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Platinum in the 2015 ranked season in 3v3 Team Ranked.”
Is the Season 2015 - 3v3 Platinum still available?
No. The Season 2015 - 3v3 Platinum was a ranked reward. To earn it, you had to reach Platinum in Twisted Treeline 3v3 during Season 5 (2015). Riot does not hand out past ranked rewards again, so you cannot earn this icon anymore.
