What does a black flag or even a solid black background with an average green star in the center represent?
(It would look much like the EZLN flag only green)
Context, please?
My first guess would be something Arab. The flags of Iraq and Syria both have green stars in proximity to black.
Or it could be as you hint, some EZLN offshoot. Perhaps the Ejército Zapatista de Liberación Vegetal.
House Atreides? 
I could have sworn there was a falcon or hawk on the Atreides banner.
In any event, the flag described doesn’t seem to be in Flags of the World’s database (I looked through anything that had a green star).