People will make references from time to time, and I expect the fashion industry will make an attempt to use the 1920's. I don't see it sticking though. Dudes aren't going to go back to wearing suits around town so soon, or calling each other "Wise Guys". The girls fashions could sneak in some places though.
But what are the other 20's stereotypes? Going to bars? Committing crimes for illegal narcotics? We already do that. The only thing I can think is that Trump is the type of dude who could recreate the Harding administration in the sense that it isn't hard to imagine a world where Trump refuses to disconnect his business dealings with the Presidency and gets caught up in corruption scandals so large they end up defining him.