To complete, here is a link to the licence for shiny 
Your code would only use shiny as a package and it is not ship with your app but required for it to run. I don't know exactly how it would apply but my understanding is you don't have to distribute your code outside the company...
If you want to publish your application inside the company but they be accessible publicly (not the code just the app), I would recommande RStudio Connect which is a pro product and a very efficient platform to publish and share R production (Rmarkdown, API, Shiny, Tensorflow, ...)