If it blinks, usually this means
a) wrong file format you try to load
b) no OpenSDA (e.g. MSD bootloader) firmware loaded
c) wrong OpenSDA firmware loaded
I suspect the later.
>>I have tried loading basically every file in Freescales quick start package while in boot mode.
What is 'boot mode' for you? To load an S19 file, the device needs to show up as 'FRDM-KL25Z' device. If it shows up as 'BOOTLOADER', then you are in the wrong mode. Plug in the KL25Z with the OpenSDA USB port. Does the device show up named "FRDM-KL25Z" as MSD Bootloader Device' (see The Freescale OpenSDA Trap: “No Device Available”, or something like that… post)? If not, then it is not in MSD mode.
To get into MSD (Mass Storage device bootloader) mode, see "Changing the Board back to MSD Bootloader (P&E OpenSDA)" in above post.
I hope this helps.