There really is no other term for this flag than spoof. It is meant to mimic the California flag with some key features changed to reflect the Star Wars fictional, or is it, universe. To borrow a phrase from Barby, AKA Paul Barbado, from Geography Now on YouTube, let’s dissect the flag!
In the upper hoist corner is an image of the Death Star which has replaced the red star that appears on the actual California flag. The Imperial Walker replaces the grizzly bear of the real flag and finally the words California Republic have been exchanged for Galactic Republic. OK, that’s the dissection but what’s the details on those symbols?
There were at least two Death Stars shown in the original Star Wars franchise, the first in Episode IV: A New Hope, and in Episode VI: Return of the Jedi. The Death Star in Episode VI was incomplete and in Episode III: Revenge of the Sith we see the original Death Star during construction. The Death Star was a mobile space station and galactic superweapon capable of destroying an entire planet, specifically Alderan was destroyed in Episode IV by laser fire from the original Death Star, DS-1. DS-1 was stated to be more than 100 km to 160 km in diameter, depending on source. It was crewed by an estimated 1.7 million military personnel and 400,000 droids. DS-2 was significantly larger, between 200 km to 400 km in diameter depending on source, and technologically more advanced than its predecessor. While DS-2 was set to destroy the forest moon of Endor in the climactic moments of Episode VI, it was destroyed before this mission could be completed.
Full details on the Death Star are available at both Wikipedia and Wookieepedia.
The walker is a bit more complicated. Depending on which sources one considers canonical, there are up to 16 different models of Imperial Walker, although the most widely known and acknowledged ones are:
AT-AT: All Terrain Armored Transport
AT-ST: All Terrain Scout Transport
AT-AP: All Terrain Attack Pod
AT-OT: All Terrain Open Transport
AT-RT: All Terrain Recon Transport
AT-TE: All Terrain Tactical Enforcer
I think it is safe to say that the Imperial Walker pictured on the flag in question is the AT-AT model.
Simply put, the Imperial Walkers are battle units that are designed to easily and safely negotiate a wide range of environments using long jointed leg units coupled with practically impenetrable armor plating and massive firepower. These units have been instrumental in several major battle scenes throughout the Star Wars franchise.
Full details on the Imperial Walkers are available at both Wikipedia and Wookieepedia.
Finally, the reference to the Galactic Republic needs an explanation.
The Galactic Republic, also commonly known as just “The Republic” refers to the interplanetary governing body in the early Star Wars universe. The Republic was able to sustain itself for over 25,000 years until the ascension of Darth Sidious, posing as a government functionary and Chairman of the Senate. Prior to this coup, and the establishment of the Galactic Empire, ruled by Darth Sidious as the Emperor, the Senate functioned to oversee the Republic as one body in the Legislative Branch of the Republic government. While the Senate was referenced in the original film, Episode IV: A New Hope, viewers are not actually taken inside the Senate until Episode I: The Phantom Menace. Once the Galactic Empire is established, it becomes common to refer to the Galactic Republic as the Old Republic. The destruction of both the Emperor and the second version of the Death Star lead to the downfall of the Galactic Empire and the rebirth of the Republic, although this renaissance will be short lived as remnants of the Galactic Empire will rise to create the equally despotic First Order.