Response article to a flawed paper you reviewed I recently reviewed an article. I found weaknesses in assumptions that meant none of the conclusions that were made could actually be made; basically they had absolutely no result. 

As such, I gave a detailed review (~ 2000 words) explaining why the assumptions made by the authors were wrong. I was civil and polite throughout, it was not an attack and I tried to remain constructive. I recommended to the editor to reject the paper and, despite recommendations of accept with major revisions from the other two reviewers, the editor rejected the paper. I believe that the authors will take the easy option and just submit to another journal without making serious edits, rather than paying serious attention too my review.

If the paper does get published in (almost) unchanged state, should/could I write some kind of response article? How does one get to do this (should I email the editor with a draft of a response article)? 

Should I contact the authors (before they publish, after they publish, or not at all, before or after I contact the editor, before or after I submit/publish a response article)?
Wait. The authors have seen your review, they should know that they have a problem. There's nothing to be done until the flawed article appears in another journal (if it ever does). You might write a draft response article and sit on it until the unchanged article appears. If it does, you can update your draft based on any changes and submit it to the same journal in response. If they fix it before resubmitting it, then you have nothing to do, and your review will have been successful.