Is it for publishing purposes or to use when developping locally ?
For a shiny app to be included, I think you must serve the application. A bookdown project can't execute a shiny app. Uploading the application onto an hosting service is the best solution, but you can also host your application only locally. That means if you serve the application, and use the http://localhost:<port> url, I think it should work while using include_app() in bookdown.
You can serve the application from your R file in another R process, for example using Background job in RStudio IDE (since 1.3).