How do you get the Season 2014 - Solo Challenger 1?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Challenger 1 in the 2014 ranked season in Solo/Duo.”
Is the Season 2014 - Solo Challenger 1 still available?
No. The Season 2014 - Solo Challenger 1 was a ranked reward. To earn it, you had to reach Challenger in Solo/Duo during Season 4 (2014). Riot does not hand out past ranked rewards again, so you cannot earn this icon anymore.
Season 2014 - Solo Challenger 1 is one of the rarest LoL summoner icons.
