Conviene comes from the verb convenir and means 'to be advisable' or 'to be a good idea'. It's a fantastic, practical word that expresses a more nuanced idea than simply 'good' or 'bad'.
In the song, Kali Uchis opens with "Dicen que no me conviene to fall in love with you" (They say it's not a good idea for me to fall in love with you). This one word immediately sets up the song's dramatic theme of a forbidden or complicated love that she decides to pursue despite the warnings.
Kali Uchis is completely defiant in this song. She knows people don't approve of her relationship, singing, "Dicen que no me conviene to fall in love with you" (They say it's not good for me to fall in love with you). But she doesn't care at all. For her, it's a simple fact: "It's too late to turn back now." She argues that nobody else can love her partner the way she does, asking, "Who cares what they love / Como te quiero yo" (Like I love you).
She admits their relationship is messy, saying, "'Cause we got issues, everyone does." She even suggests that drama is a necessary part of real love with the line, "Si no hay drama no hay amor" (If there's no drama, there's no love). But right now, she's tired of the conflict. She just wants to move past the arguments and get physical, bluntly stating, "Ya no quiero más problemas / Te quiero en la cama y sin más complicación" (I don't want any more problems / I want you in bed and without any more complications).