術 is read as すべ here, an elegant and somewhat literary word meaning “a way” or “the means to do something.” In the song, 飛べる術くれて means “you gave me the means to fly,” portraying love as something that gives the singer the power to overcome despair.
This is BTS begging someone to pull them out of a dark night, and the Japanese version doesn't waste a second. It opens with "息詰まりそうさ 今にも" (I feel like I could suffocate any moment now) and "夢ならいっそ やめたいよ" (if this is a dream, I'd rather just quit it). There's nowhere left to go, and the cause is simple: "君がここにいない それだけでもう" (you're not here, and that alone is enough). The singer feels close to freezing and asks you to "暖めて" (warm me up), "もっと もっと" (more, more). Then comes the chorus everyone shouts along to: "その手を出して" (hold out your hand), followed by the English "Save me, save me".
The second half turns from panic to gratitude, and that switch is the best part. Looking at the moon, the light is "眩しくて so lunatic" (so dazzling), a fun bit of wordplay since lunatic comes from luna, the moon. Just remembering this person means "何も怖くない" (nothing is scary). The rap section is a long thank-you list built on the verb くれる (to give me, or do something for me): "飛べる術くれて" (you gave me a way to fly), "翼すらくれて" (you even gave me wings), "目覚めさせてくれて" (you woke me up). If you're learning Japanese, that 〜てくれて pattern is worth stealing. It ends on "Thank you 君が全て" (thank you, you're everything), which is a bit much, and completely sincere.