After a restart the flash still did not work, however it did work on my flashlight widget.
Even though no one encountered this problem, I thought I'd leave the solution that worked for me in case any people are Googling to get here:
The support tech had me reset the phone by taking the battery out. That did not work.
Then they had me go to Settings, Apps, All Apps, Camera.
In the camera app section, press "Clear Data".
This fixed it.