Do you have an older android source code of your phone or only the linux.
In case you have an older android version source code, you could start with doing a diff of the kitkat and the android source as given by the vendor and identify the elements that have been added/modified by the vendor. Once you get a feel of it, you need to either identify components and start porting them to the kitkat source from the vendor provided source. Most notably you might have to start with providing your product directory ( follow the crepso or the MSM products done in the AOSP ).
If you do not have the android source and only the linux source code, then be prepared for a huge assignment.....you basically have to identify each components, dig deep in the hardware dir of the AOSP and start integrating the linux device drivers + native libararies in the AOSP first followed by making relevant changes if any in the upper layers of the framework.