It's partly a matter of becoming familiar with the way different people spoke during the period and knowing the difference between people who speak naturally and the ones who were putting extra work into being slicker than an icy road on bald tires. There was never a time when people who insisted on talking like Beatniks or Bolsheviks didn't cause a lot of eye-rolling. It's authentic for their utterances to be cringe.

Some of it goes in and out of fashion very quickly, while others hang around for generations. WW II G. I. slang was especially durable because it was common to a huge swath of people, while slang associated with fad, fashions, and movements tends to fade almost as soon as they do.

The Hollywood movies and pulp fiction written at the time are a pretty good start. They're not really representative, but at least they're contemporary, and they're what readers will compare your own efforts to unless they're especially old or well-read.