If you are compiling Kitkat or an earlier version, I'll need JDK 6 (preferable Oracle release). If building Lollipop, use OpenJDK 7 (I tried Oracle JDK 7, and had problems).
About kernel img and drivers, you can extract from any available iso (the one I posted here has goodix, for example). To do this, you can:
1) Download the iso you want to extract kernel img and drivers;
2) create a dir and mount iso on it:
Ex:
mkdir mount1
sudo mount android_x86.iso mount1 -o loop
3) Inside the mounted dir I'll have the kernel img, initrd, ramdisk. You can copy them to your img
There's also system.sfs, the /system img file, which you can also mount
mkdir mount2
sudo mount mount1/system.sfs mount2 -o loop
4) Inside mount2 I'll have a file named system.img, which you can also mount
mkdir mount3
sudo mount mount2/system.img mount3 -o loop
Here you can get lib/modules (kernel drivers) and lib/firmware (firmware files required for some devices)
Note: Not sure if just copying kernel img + modules will work. Some apps are "linked" with kernel during compiling.
The best practice is compiling your own kernel
Regards,
Pstglia