Hi Avner
The AN4370 SW does include a KL25 target but it doesn't say which board the KL25 is on. The only thing that I have seen is a note stating that for USB functionality J17: P5V_K25_USB should be set. There is no J17 on the FRDM-KL25Z so I expect that the software was developed for a different board (although there is also no J17 with this connection on either the TWR-KL25 or the TWR-SER board).
I would however ask whether you really want/need to use USB-DFU since it is an immensly complicated method to do firmware upgrades due to the fact that it requires you to develop/customise a PC application (usually multiple such developments if you want MAC and Linux users to be able to do it too), a boot loader software supporting DFU and 'also' develop DFU support in the application that you are updating if you want to do it right according to the class. Personally I don't see the attraction for typical usage but only for maybe a company like Logitec who can invest several months of development and personalisation so that they can give a slick and cool firmware updating experience for their users (since the sell enough such devices to make it worth while and they need to keep their image highly polished).
For "standard" firmware updating Freescale offers their Kboot (with a USB-HID application) or you can use USB-MSD (the most popular method which requires absolutely no PC software to be installed on any OSs) or plug in a memory stick (USB-host).
You can try USB-MSD and Kboot USB with the binary at http://www.utasker.com/kinetis/FRDM-KL25Z.html
and verify that your FRDM-KL25Z HW is operational in the process.
It is possible to use USB-MSD, USB-KBOOT and USB-Host (memory stick) at the same time if desired and you can avoid any software development if your goal is not specifically to learn building such loaders for educational reasons.
Regards
Mark