The term ironic derives from the Greek word ειρωνικό (ironiko). The term iconoclastic (εικονοκλαστικός) derives from an originally religious (which then developed into poltical) conflict in the Byzantine empire, during the 8th and 9th Century CE, over the use of icons in religious worship. There were two camps. The iconoclastics (also known as iconomachous, or battlers against icons), on the one hand, were opposed to the use of religious imagery (except for purely symbolic imagery like crucifixes) and the iconophilous (also known as iconolatris, or worshippers of icons) on the other hand were for the use of religious icons. Anybody that has been to an Orthodox church will be quite aware of who won the conflict.
So, ironoclastic or ironiclastic? Well, the word does not exist in greek, but if it were to exist it would be ironioclastic and would basically mean somebody that is opposed to irony. This, though, seems to be the opposite meaning of the one people are trying to give. I would consider Zen to be ironiophilic (also not a real word) ie friendly towards irony.
Zen is iconically iconoclastic
Seems to be true for those that try
to be iconoclastic (and it seems there are quite a few try-hard iconoclasts in the field of American Zen). I imagine though, that the mad zen masters who have realised this form of being, are not at all iconic, that their iconoclasm is real. Those that use iconoclasm to justify their (unwholesome) behaviour though... in Tibetan Buddhism we have a special hell reserved for people like that.