I feel that so-called "prophetic" dreams are actually a specific instance of deja vu.
And I feel that deja vu is a malfunction of the circuits in the brain responsible for recognition.
It is well known that there are areas of the brain that "light up" when you recognise something - whether it be a sight, or a smell, or a taste, or a thought. There are people who have had this area of the brain damaged, and they cannot recognise anything.
My hypothesis (and I admit that I haven't the facilities to test this) is that deja vu is a brief misfiring or a malfunction of this recognition center in the brain. It makes us believe that we recognise something when it actually hasn't happened to us before.
I once had a deja vu experience of having a deja vu experience... of having a deja vu experience... of having a deja vu experience... I think you can see where this is going. The original experience which sparked the original deja vu is long forgotten. But I had this recurring deja vu seven times. That is - I have a memory of recognising the experience for the seventh time. I think I also have a dim memory of the sixth time, but apart from the certain knowledge of the number of times, the early ones are now lost to my memory.
Prophetic dreams are simply another manifestation of deja vu. You may or may not have dreamt something similar to the situation, but the recognition circuit fires and you experience the deja vu. Researchers now understand that memories are not explicitly stored in the brain - they are reconstructed "on request" as it were, and are frequently modified in the process. When the recognition circuit misfires in response to a particular trigger, the brain manufactures a suitable memory, and modifies it as necessary to closer resemble the trigger for the recognition impulse, because after all, it was "recognised".
So the "prophetic dream" may or may not have been an actual dream you had. If it was, it may or may not have closely resembled the event that triggered the deja vu. But the deja vu process makes it resemble the trigger event. If necessary, the deja vu process can manufacture the memory from whole cloth.
That's my theory, anyway. Until we get a device where we can play someone's dream on a screen, I don't see how it's testable. But I think it is at least plausible given what I know about neurology and how memory works.