Why does it sound perfectly natural to say Our flight leaves tomorrow at 6pm but weird to say It rains tomorrow at 6pm? What kind of scenario, if any, could make the rain sentence sound natural?
In continuation with the surety-prediction advocated in the other responses, you might also argue that we never know with a 100% confidence that the flight actually leaves at 6pm tomorrow.
The technically correct usage would be (and because the flight schedule is present) -
"The flight is scheduled to leave at 6pm tomorrow."
"As per the schedule, the flight leaves at 6pm tomorrow."
But for all purposes of common usage, the sentence you quoted in the question suffices for audience communication.
Regarding your query for the rain situation, the only situation where it would sound appropriate, was it coming from a soothsayer, an oracle or a psychic predicting tomorrow's weather. I guess it is within their business obligations to use such sentences to sound mighty-sure and give themselves an aura of invincibility against nature's vagaries.
Even “it will rain tomorrow at 6pm” sounds wrong, for the same reason Ham and Bacon states—it’s not a known thing. In the former example, though, you’re technically describing a schedule, something that exists in the present, so the present tense can be appropriately used there.
The reason it is natural is because the fact that the flight is leaving tomorrow at 6p.m. is absolutely known for sure, whereas you are only predicting that it might rain. You can't be entirely sure that it is going to rain, so "will" is used to note that you are predicting it.