Hi
Unfortunately I don't think that you have the experience to be able to use the uTasker code in our project so you may need to debug and adapt the example that you have from the K22FN512. You already know that it doesn't run on the K22FN128 so you need to investigate why not and what needs to be changed.
Initially you need to start with an analysis of the clock configuration since it sounds as though the FRDM-K22F example is using the PLL, which doesn't exist in the K22FN128:


Top is from K22FN512 - bottom is from K22FN128 (note the absence of the PLL).
You can also try to configure the original FRDM-K22F project to use the IRC48M (crystal-less) because then the clocking would already be the same and then moving to the K22FN128 will be a smaller step.
In the uTasker project this is selected by a define:
#define USB_CRYSTAL_LESS // use 48MHz IRC as USB source (according to Freescale AN4905 - only possible in device mode) - this should always be used if not external !!
but it may be that the FRDM-K22F examples don't support this and so needs to be copied from other sources or developed form the ground up. There is a reference to crystal-less mode (and potential erratas that need to be worked around) at: http://www.utasker.com/kinetis/MCG.html
Beware also that the K22FN128 can only be used as USB device and can't be used a USB host unless a dedicated 48MHz oscillator input is supplied!
In fact the reference binary that I linked to is already using crystal-less mode on the FRDM-K22F and so would also run on your K22FN128. I can send you an operating project for your chip (and board) but it would need the ability on your behalf to add the library code to your project. A simpler technique is usually to take your existing application code and insert it into the uTasker framework since this avoids any complications, gives optimised drivers and the capability to simulate the complete operation which reduces development time and effort (and saves costs in professional work).
Regards
Mark