No disrespect, may be I am getting something wrong but I think this scenario is not possible, because of multiple reasons. First objects cannot travel at the speed of light as you have already said earlier, but even if something hypothetically did travel at the speed of light and then object A flashed a light beam, the photons from that source will never reach object b as they cannot travel faster than their speed of light. A third object might see both object A and object B and also see the light beam from A colour shifted due dopplers effect.
BTW I do realize the whole scenario is very hypothetical as no perception of time would exist for any object travelling at the speed of light.