Does the beast warn Simon of his destiny/fate?
Yes, indeed he does. Simon knows, the beast says, that the beast is a part of the boys themselves, and the beast warns him to run away and not to share his knowledge with the others.
“I’m warning you. I’m going to get angry. D’you see? You’re not wanted. Understand? We are going to have fun on this island. Understand?
We are going to have fun on this island! So don’t try it on, my poor misguided boy, or else—”
Simon found he was looking into a vast mouth. There was blackness within, a blackness that spread.
“—Or else,” said the Lord of the Flies, “we shall do you? See? Jack and Roger and Maurice and Robert and Bill and Piggy and Ralph. Do you. See?”
Simon was inside the mouth. He fell down and lost consciousness.
Of course, Jack and Roger and co. do "do" Simon: they kill him in a mock beast hunt. And it is exactly because of the beast within: which they think they are killing, that Simon is killed. So it makes sense for him to fall down inside an imaginary version of a "vast mouth", a "dark" mouth: the mouth of the beast, of the darkness within people. Simon is about to become a victim of darkness.