At the heart of FlySight is an AT90USB microcontroller. The datasheet for the AT90USB family can be found here:
The firmware is written in C, and can be compiled using AVR-GCC. If you're using Windows, the tool of choice is WinAVR:
WinAVR includes a simple editor called Programmer's Notepad, which makes it easy to compile the source. Once it's compiled, you'll need to program the FlySight itself. This is described in further detail here.