Al chile is popular Mexican slang that means "for real" or "honestly". The literal translation, "to the chili pepper", makes it a fun and memorable phrase that doesn't make logical sense on its own!
In the song, Xavi sings, "Al chile, que te vaya bien". He uses this slang to add a raw, honest punch to the final goodbye, essentially saying, "For real, I hope it goes well for you." It's a fantastic phrase to learn if you want to sound more like a native speaker from Mexico.
In "Corazón De Piedra", Mexican singer Xavi is completely done dealing with drama, and he is not holding back. The title translates to "Heart of Stone," pointing straight at an ex who never realized how much he actually cared until everything fell apart. Instead of begging her to stay, Xavi delivers a blunt kiss-off. He tells her "Lo que tiro no vuelvo a recoger" [What I throw away, I don't pick back up] and reminds her that he wasn't born yesterday ("mija, no nací ayer"). To really clear the air, he uses some sharp Mexican slang, saying he is not here for her nonsense ("pa' tus mamadas") and bluntly wrapping things up with "Al chile, que te vaya bien" [For real / Honestly, I hope things go well for you]. In Mexico, "al chile" means being totally frank and telling it straight like it is.
There is a great contrast here between his bruised feelings and his newfound pride. He admits he deleted all the photos and messages ("Borré las fotos y los mensajes"), yet he also warns her that there is already a line of people waiting behind her ("Hay fila atrás de ti"). Even though it hurts that she had such a cold, stony heart while he was genuinely in love, Xavi refuses to waste another second. If she wants to walk out the door, he is more than happy to let her leave.