This is the quintessential Relativity question, not really a mind blowing speed of light question. If you are witnessing the traveler zooming by you at the speed of light and they turn on their flashlight, the light does not escape the end flash light due the fact that nothing moves faster than the speed of light. Even a light of a flashlight that is turned on cannot go faster than the speed of light. It's the Law!
Here is the Relativity part. When the traveler himself, turns on the flashlight the light itself behaves just as it would normally. The light shines forward at the speed of light ahead of the vehicle. This occurs because the flashlight is stationary relative to the traveler. It is going zero miles per hour relative to the traveler. It's all relative. Different results but true to the laws of physics, Relative to the Observer. You cannot observe from outside of the vehicle and also observe from inside the vehicle at the same time so you see no paradox.
This is not how it appears. It is how it is. That is what Relativity is all about