i have the same problem- updated my iPhone 6+ a few days ago to 9.3.1 and now Flashlight symbol is greyed out- no go!
Where does this app and possible settings reside? thanks
Perform a hard reset (does not delete any data on the phone): Press and hold down both Home and Power buttons at the same time until you see the Apple logo. Then let go and allow the phone to reboot itself. If that doesn't work you'll need to factory reset (deletes all data) and then restore (restores all your data) from your last backup.