So in general you can do something like the following
<div id="visualization" ondblclick="alert(1)"></div>
This will work in image based charts, table, map and a few others.
As far as I know it won't work for the interactive charts as they are iframed.
Moreover, as the interactive charts funcitonality does not include interaction with a user double-click I am not sure we intend to expose this event in the future.
This should work and will alert 1 on every double click your visualization gets.