Is Codenames meant to played in American English, British English, Australian English, or any of them?
Codenames was designed by Vlaada Chvatil, a Czech game designer, and in its original form was published by Czech games edition. So in that sense, the answer is none of the above.

More generally, the best clues in Codenames are the ones that will lead your team to guess the right words, which means you should assume that you are playing in whatever version makes sense for the players. This can include consideration of things like pop culture references (will your team understand that "Mine" is a clue for "Seagull" because if Finding Nemo?), but also deeper cultural associations.

If your team is all from the US, you should feel safe using American English as the baseline for your clues. If you don't know whether your fellow players speak American, Australian, British, Singaporean, Canadian, whatever English, then you have to use clues that are (to your knowledge) as common across them all and hope for the best.