This Gist provide the function to retrieve the local IP address of the device when connected to the wifi.
No permission is required from the user to access the information. It uses the getifaddrs method that is not directly part of the public iOS API but it's still perfectly fine to use it and allowed by Apple.
https://web.archive.org/web/20160527165909/http://www.makebetterthings.com/iphone/how-to-find-ip-address-of-iphone/ https://stackoverflow.com/questions/6807788/how-to-get-ip-address-of-iphone-programmatically
The following permission is required in your AndroidManifest.xml:
https://stackoverflow.com/questions/16730711/get-my-wifi-ip-address-android