Using the built-in LED flash while recording video on iOS can help illuminate a dark scene or highlight your subject. Unfortunately, it's impossible to switch the flash on or off while recording is in progress. The Camera app hides the flash toggle option as soon as the record button is pressed. This means that the choice of whether to turn the flash on or off must be made before recording begins.
The free jailbreak tweak Record 'n' Torch seeks to improve the situation by adding a moveable flash toggle button to the video recording screen. The button can be dragged to different places on the screen, and when tapped it will turn the flash on or off while the video is being recorded. To remind you the flash is switched on, the button even turns yellow.
Record 'n' Torch provides the option to disable the video flash button under Settings, and an option to switch off the Camera dismiss gesture. For example, when using the camera from the lock screen, the camera app can be quickly closed by swiping from the top of the screen. Turning off the gesture prevents the recording from being accidentally interrupted while dragging or tapping the video flash button.
Record 'n' Torch is available on Cydia from the BigBoss repo free of charge. Check here for instructions on how to jailbreak iOS 6.x with evasi0n. You can also find out how to purchase and install Cydia tweaks with this guide.