Westray-Papa Westray is the world's shortest scheduled flight, as mentioned in the article. I don't think it's possible to get any shorter than the 2 minutes it takes to get from PPW-WRY as even then it's usually not even half that time.
For me the shortest scheduled flight I have been on has to be Akureyri-Grimsey in Iceland which was scheduled to take 30 minutes but took barely 19.