She's fuming about the idea of Gaebril or ANY MAN sitting on the chair. Note that the dream doesn't imply anything to come or suggest any importance to her anger - the significant thing is that Rand is going to sit on a throne, and apparently the dream editors are so out of touch with humanity and reality that they missed the significance that it was a throne, so when they tried to figure out why it was important, came up with the datum about the owner being angry, so they passed that on to Egwene by way of "clarification."

Or the anger of the chair's rightful owner could have just been intended to represent to the readers that Rand is not going to rule Andor and he's not going to turn down the throne just because his girlfriend wants it - rather it shows the important reason why he's not going to rule Andor - that he won't be accepted as the rightful monarch.

All in all, I'd say that dream was simply meant to service tFoH, and not the series as a whole. The end of tFoH was pretty much the high point of Rand's career as the Dragon Reborn, and in the prologue of the very next book, Min makes that point, summing up the perspective of readers too dim to catch all the ominous foreshadowing, or make an objective assessment of the situation. I think the dream, and Morgase's last thought were intended just to signal to the readers that not everything is going to be wine and roses from here on out. Bashere & Rand discuss that notion in their dialogue, but let's face it: to the typical reader, the idea of Rand conquering the world at the head of an army of Aryan ninjas and male channelers, with a couple of genius military commanders at his side is hardly the daunting prospect that Rand, Bashere or any sensible person who has to live in the world of WoT would find it. These same readers take Rand's words "Peace is far off yet. It will be blood and death for some time to come" as a promise of Action in the books ahead, and they have hardly grown up by the time CoT rolls around 10 years later, as evidenced by their bitching that nothing happens in it.

So in order to suggest the downer books ahead, we have stuff like that dream and Morgase's views on the subject to hint that there's hard times to come.