The hardest to find patches by far without a doubt are Star Wars military themed patches. Yes, the United States government and branches of the military and even foreign military branches sometimes idolize Star Wars in thread and stitch as well. In my 40 plus years of experience collecting Star Wars patches hardcore, nothing is harder to obtain than specific armed forces Star Wars themed patches.
Foreign or domestic both are just so scarce.
It is hard to determine how many are produced and there are not many styles and examples available that exist; mainly because these patches almost never hit the public sector and are close to impossible to acquire (“unless you fly an F-16 Fighter Jet everyday for a living”). Most Star Wars military themed patches are job and class specific and could only have a run of 10-15 or even less depending on the government.
Enthusiasts in the last 10 years have seen a rise in the morale genre focusing on pride, service and dedication which also have become exclusive and limited.
Basic training has just begun for you my patch padawan apprentice and you will no doubt have more questions than answers when you are done;
try not to gasp as you gaze upon forces you have never seen before!