In English, the example I would proffer is “attorney general”, which as-written refers to the chief lawyer that advises a state (sometimes exceedingly badly). But if reversed, “general attorney” could plausibly refer to a lawyer that can take on any type of legal work, not self-limited to ones within a particular specialty (eg divorce law, personal injury, copyright, etc).

This is in the realm of postnominal adjectives, although not all reversals will yield recognizable phrases, and some will be nonsensical, like “the incarnate devil”.

I have a suspicion that the closest that English gets to the Japanese kanji-switch might be in technical writing, specifically for the name for pharmaceuticals. Such names are often order-specific, because they draw from the chemical structure of a molecule. From the minimal Japanese that I know – thanks anime! – I’m aware that the word for “carbon monoxide” is composed of one carbon and one oxygen. But if I were a chemist or pharmacist, I might recognize the root components in the names “paracetamol” and “acetaminophen”, which are the same thing.