How do you get the Season 2016 - Solo Diamond?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Diamond in the 2016 Ranked Season in Solo.”
Is the Season 2016 - Solo Diamond still available?
No. The Season 2016 - Solo Diamond was a ranked reward. To earn it, you had to reach Diamond in Solo/Duo during Season 6 (2016). Riot does not hand out past ranked rewards again, so you cannot earn this icon anymore.
