I was expecting there to be something that popped up to stop me from re-buying a unique skin I already had, but this did not happen. I was able to buy a unique skin (Ice Berserker) from the Rewards tab of the season 1.2 page even though I’d already bought it in season 1.1.
I have only tried it once, and not with any other skins.
I have the Minotaur Berserker, who did not have the ice skin equipped, though I was using a Necromancer character at the time.
Not mentioned in here but @Arkanzier had also submitted a ticket where we investigated this further.
A fix is on the way to prevent duplicate skins from being purchased in future.
As for what you are experiencing @AeonNhiyr, if you haven’t already can you submit a ticket with a screenshot of it displaying as being purchased and another (if possible) of it being unavailable to equip?