You can't really find out how many times your links show up in a One-Box result but you can see how much traffic is coming in from those links by using the ved parameter in the referrer query string. This is a little complicated to explain in a single post but I'll wrap it up and provide links to articles you can read to fully understand how to do this.
Each link on the Google SERP contains a referral parameter with a value that contains information about that link. This value can be captured and analyzed for details on where the link was located on the SERP. The value is stored in the "ved" parameter. Various types of SERP links standard results, One-Box, sitelink, breadcrumb, adword, knowledge graph link, etc.
This article on the Moz blog from David Kelly has a good summary and tells some back info on Tim Resnik's work on first noticing patterns in the ved parameter and trying to decode them. http://moz.com/blog/inside-googles-ved-parameter
Here's a link referenced in that article that goes deeper on decoding these ved values: https://deedpolloffice.com/blog/articles/decoding-ved-parameter
And here's yet another series from Benjamin Schulz on decoding these values: http://gqs-decoder.blogspot.com/2013/08/google-referrer-query-strings-debunked-part-1.html
This is very cool stuff if you get into it. Good luck!