Theres no way Kim dies
The show keeps teasing it cause they know we know shes not in Breaking Bad, but they wont ever actually do it.
Mainly cause i couldn't picture Saul being the upbeat cheery charisma oozing lawyer he is Breaking Bad if Kim was killed cause of him, i just couldn't picture him being able to live with himself, let alone continue to be Saul Goodman and going on as if she never existed in Breaking Bad.
To me she either just realizes how much of a bad person Saul is and leaves him, or it gets to the point where she is gonna die has to see the vacuum guy and get a new identity. But theres no way she dies, Jimmy would never be the same imo if she did.
Infact i think shes gonna show up in present day and find Gene and its gonna lead into the post Breaking Bad show dealing with Saul trying to protect his identity and dealing with Kim back in his life, cause that shows gonna need some familiar characters in it, and if we can't have Jesse or Walt its gotta be Kim from BCS.