Yes, there are "flashes" made for smart phones (to clarify terminology.... flash is for still images, and must be synchronized to go off when the shutter clicks. Video requires steady illumination).
There are a number of products for iPhone that are intended to be used for both still and video images - they're typically small panels containing multiple LED lamps, and often plug into the headphone jack. I haven't used any, so I don't have recommendations.
When it comes to shooting video, think in terms of "supplemental lighting" rather than single-point illumination attached to the camera (which would cast strong shadows that move about as the camera moves).