I've never seen an interview before maybe 20 years ago where he makes that claim at all, but I'll admit that something could exist and I could just be wrong. Anyway, to start I'd say that Star Wars is generally apolitical: the big evil empire follow the ideology of being evil and want to control the galaxy because they are evil, the rebels are the good guys who fight for good. As a result, looking to the text for political parallels isn't really possible, instead leaving us with the much mushier realm of vibes and aesthetics. To run through some points:

• Lucas was inspired by lots of WWII films (see this article for a few examples), and basically just incorporated whatever he thought looked cool (like the rebel award ceremony in ANH being inspired by fucking Triumph of the Will. This leads to many thing being US (or maybe Allies)-coded, because most films he would have seen would have been about the americans/allies in WWII, with american/allied planes.
• Similarly, the main climax of two of the movies are big space battles. IIRC the vietnamese airforce was tiny, leading to very few aerial engagements, while WWII had many famous aerial battles.
• The war between empire and rebels is depicted as an existential struggle between good and evil. Nazis serve as the cultural shorthand for generic evil, which makes the rebels the allies by default.
• Vader is really close to the german "vater" for father.
• In RotJ the rebels launch a guerilla attack in a forest using the local indigenous people and their relatively low-tech weaponry to clown on the empire. This type of thing doesn't really occur in the two preceding movies.
• Low-hanging fruit, but all of the main characters are white.

The one easy counter I'll concede is that tie fighters are clearly an analogy for carrier-based planes.