Oh wow. I'd always just assumed it was a US idiom along the lines of yada yada or something. Buffalo buffalo... doesn't work in British English as it is only a noun.
Nearest English silliness I can remember hearing is: police police police police.
FWIW I'm an ESL speaker from a non-English speaking country and despite having had endless exposure to (mostly American and British) English since a young age, I've never encountered the verb form of "buffalo" outside that one sentence. It's an informal North American idiom and by international standards apparently a fairly obscure one.
Policing OTOH seems to be a fairly widespread verb form with a clearly understood meaning (i.e. what the police conceptually is supposed to be doing). Unless you have close experience with buffalo, you probably can't infer buffaloing means "intimidating".
EDIT: Also as mentioned elsewhere, not everyone outside the US knows there are places actually called Buffalo or makes that leap when hearing the word "buffalo". So "Buffalo buffalo" is more likely to be read as "buffalo(n) buffalo(v)" (which already sounds weird if you don't already know what "to buffalo sb" means) which breaks down as soon as you add more buffalo to the sentence.
It’s extremely obscure as a verb in North America too, fwiw.
Buffalo the city was probably better known 150 years ago, when it was an economic powerhouse as one of the end points of what’s still the second most famous canal in the Western Hemisphere. Afterward it continued to be a significant industrial center until the decline of manufacturing turned the Great Lakes region into part of the “Rust Belt” in the past 50 years. Most Americans probably know of it these days because it still hosts an American football team.
Anyway, the point isn’t that that’s a common sentence. It’s that it’s a grammatical one.
Of course nouns have been made verbs in English. You'll find no British English dictionary listing where buffalo is, unless noting US usage, where it is both.
Police police police police is grammatically correct, but of little meaning : (the) police police(v) police (of) police (ie overseers of the police).
[1]: https://en.m.wikipedia.org/wiki/Buffalo_buffalo_Buffalo_buff...