Kid isn't a true "clone" of Schala.
Kid is unique from Schala. Kidd has a different hair color, bordering orange, and her eye color is different. Also, her personality is way unpolished compared to Schala.
However, Schala magically created Kid in a last ditch effort, as Zeality said, to preserve her sanity/good side before Lavos could fully integrate with her mind.
Kid is used by Belthasar to achieve his plan. In the original CC timeline, Serge died, but Kid was sent out of the DBT regardless. Sometime after 1020, Belthasar met her and told her to go back in time, to 1020 to call Serge into Another World. Supposedly, when Kid did this, she left and went back to her time, and then the Kid from the current period arrived at the scene to meet Serge (probably as a coincidence as she was investigating into Lucca's death).
Kid lives on to avenge Lucca's death, as she was found and raised by Lucca as a baby after Schala sent her from the DBT.
Kid cannot die as Schala's pendant sends her back into the immediate past before she is killed (that or she is teleported somewhere else because otherwise there would just be a loop if she went back in time, and got killed again lol).
@ Kyronea - Marle's pendant isn't the same as Schala's. Marle's pendant is Schala's pendant from the original timeline, a pendant that had all of it's power drained, and we do not know any of the details how Schala lost it etc. However, Kids pendant is Schala's pendant from the altered timeline, where Schala fell into the DBT. I hypothesized that being in contact with Lavos and the Mammon Machine as she fell in, her amulet was probably overwhelmed in Lavos' power or something, and thats why it's even more different than the first.