Here, I will stubbornly (for a while at least) dig in my heals. If he points his flashlight toward the front end of the ship, and he's already traveling at virtually lightspeed ... well, if he sees a "normal" beam of light, it will take him years (from a "stationary" observer's viewpoint), maybe millions of years, to achieve that perception. But you're right, I suppose that's what he will see. He won't see a luminous blob slowly emerge from the flashlight, because he and the blob are both operating in the same time. But if you and I were "stationary" and watching him fly by, we wouldn't think he was getting much pizzazz out of his flashlight.
On the other hand, if he points the flashlight toward the rear of his ship, once again he'll see just what you say -- the beam will travel at the speed of light. But (am I right in this?) a stationary observer should see that too.
Great question! Now: How do the observers each know where the leading end of the light beam is, at any given time?
(Hint: "at any given time" is a bear trap of a phrase.)