How do I activate the flashlight during a front-facing camera recording? How do I activate the rear-facing flashlight during a front-facing camera recording on the iPhone?
It seems you can't.

As soon as you press the record button, the option to enable the torch or flash is disabled everywhere. You must decide whether you need any extra brightness beforehand.

Check this link for more info. Note that what @dwightk said in the comments was spot-on, except that instead of apps there are jailbreaks available if you really need this control...