Flechándome comes from the verb flechar, literally 'to shoot with an arrow'.
The song says Cupido flechándome, conjuring the vivid, romantic image of Cupid mid-shot, the exact instant love strikes. Its unusual gerund-plus-pronoun form makes it memorable and a great entry point to learn how Spanish packs action and object into a single, expressive word.
Have you ever met someone and felt an instant connection? Morat's "En Un Sólo Dia" is all about that whirlwind feeling of falling for someone in a single night. The story starts in a bar, where the singer tímidamente [shyly] asks someone to dance. They spend the night dancing bachata, merengue, and boleros, hablando bajito, chocando los cuerpos [talking quietly, bodies bumping together]. It's so intense that he feels like Cupid has shot him with an arrow.
The party ends, and they both go home, but for him, it's just the beginning. He leaves con tu cara pegada en el alma [with your face stuck in my soul] and immediately starts to miss her. The song's main idea is this surprise and confusion: Tal parece que yo me acostumbré a ti en un sólo día [It seems I got used to you in just one day]. He feels like he's known her for years, breaking all the usual rules of love and time.