My understanding of how Shiny Server works is that your apps are run by default as a user called shiny. This means the shiny user on your server needs to be able to read the files. Even though you gave permission to write to /srv/shiny-server, you still need the change permissions so shiny can read them.
The simplest solution is to use chmod to grant permissions to the files and folder. You can use something like this:
Chmod 777 -R /srv/shiny-server/appname
Keep in mind you need to run that command as either root or as the user who created the files.