Just ran into this, trying out the Galileo on some of my own code.
Suggestion:
Do like some other non-avr Arduino setups have done and create a file avr/pgmspace.h inside of your include directory.
With the chipkit (pic32) version of the IDE (MPIDE), they created a dummy file that did not do anything, other than to define that it was loaded. On this platform, detecting it was on this platform and defining my own versions of the pgm_ macros like the Teensy did.
With the Teensy addition to the Arduino IDE, they also created a file at this location, that simply defined some(all?) of the main pgm_ macros, knowing there is only one memory space. Example:
#define pgm_read_byte(addr) (*(const unsigned char *)(addr))
I did something similar when I ported some of my own code over to run on some other Linux boxes such as the Raspberry Pi. This allows me to continue to share most of the code on the different platforms.
Next up, see what defines are in place so I can detect I am building for the Galileo and try to fix.