The picture is from a bathroom in the Bellevue adult outpatient medicine clinics. I also know the phrases apretar el botón or tirar [de] la cadena - but I like floshar much better.
In our Yiddish at home we say aroplozn dos vaser; I know people have also said (op)shvenkn dem klozet. Of course, just like American Spanish, in American Yiddish nowadays 99% of people say (I bet) floshn. I use that word too, with guilty pleasure.