I am pretty sure Kult's not currently in print from anyone, and I'm reasonably familiar with the US publication history. However, I haven't been able to find any information on plans, attempts, or dreams regarding republication in English or anywhere else. It may be one of those legions of 1990s games that doesn't have a fan base to sustain a reprint, but I'd be interested if anyone was trying.
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It seems to be owned by Paradox Entertainment, but they seem more concerned with licensing, so my guess is that you'll see a Kult film or TV series before you see a new edition of the rpg.
There appears to be an active fan community at The Last Cycle, and they will probably know all the details.
According to the Kickstarter page, the text is ready in swedish and is being translated to English. It should be available by December 2016 to pledgers (no estimate for public release is mentioned).