Thanks for using Apple Support Communities. It's my understanding that the Flashlight and Camera options have stopped working on a your iPhone Lock screen. You've done a great job trying to get this resolved. I'm happy to help.
I recommend you reinstall the iPhone iOS with iTunes. This step can resolve possible software issues. When reinstalling iOS, iTunes will completely remove your current software and install a fresh version. While iTunes will try to do this without removing data, it's a good idea to make sure you have a recent backup before trying this step.
How to back up your iPhone, iPad, and iPod touch
Use the steps in the link below to reinstall iOS with iTunes:
If you can't update or restore your iPhone, iPad, or iPod touch
Let us know the results. Please include any other troubleshooting steps you may have tried.
Have a great day!