Working backwards through the errors:
firmware-privaFastLED/led_sysdefs.h:19 is including a header that should only be included on an AVR. It’s getting there by default because STM32F10X_MD isn’t defined when compiling for the Photon. You could figure out what equivalent definition is set by the compiler for the STM32F2xx and add that to the header, but that would probably just expose another incompatibility.
@dgarcia didn’t make it to Maker Faire, can someone on the Particle team make sure he gets a Photon ASAP? (Pinging @zach ) I’d volunteer one of mine but it has to get to NYC first, then head right back to the Bay Area.