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Melisandre repeatedly tells Stannis that the fires have shown her that he is the Prince foretold to save them. She also tells Stannis that he must turn over Edric Storm, and then later Mance Rayder's son, as they carry "the blood of kings", claiming that sacrificing a child with the blood of kings will "wake the dragon from the stone".

However, Daenerys has already woken three dragons from the stone (the stone eggs), using the sacrifice of a child with the blood of kings (her unborn son).

Is it possible that Melisandre simply got the visions of her flames confused, and Stannis is not who she thinks he is supposed to be?

So far there is no definitive answer in the books who the Prince That Was Promised is. Also, it is not clear whether or not Melisandre knows about Daenerys and her dragons. However, there are definite indications that Milisandre's interpretations of her visions are not always correct.

For example, in "A Dance With Dragons"

Melisandre predicts that Arya is about to arrive to Castle Black, but it turns out to be Alys Karstark.

There are also indications that Stannis is not Azor Ahai reborn. For example,

his sword "Lightbringer" is a fake, as determined by Maester Aemon.

Possible candidates of who Azor Ahai reborn might be are listed (warning! spoilers!) here.

Melisandre believes in the prophecy, and she believes very firmly that Stannis is Azor Ahai. Maester Aemon (AFFC) has the answer -- or one of the answers -- that you are looking for, and I happen to believe in: That Melisandre sees what she wants to see. She is ambitious and skilled, but she pushes for results -- as we have seen many times -- and thereby also forces her opinions on what she sees. She "helps" the truth along.

As Maester Aemon says (p. 521 A Feast for Crows):

Daenerys is the one, born amidst salt and smoke. The dragons prove it.

[...]

The prophecy... my brother's dream... Lady Melisandre has misread the signs. Stannis... Stannis has some of the dragon blood in him, yes. His brothers did as well. Rhaelle, Egg's little girl, she was how they came by it... their father's mother... she used to call me Uncle Maester when she was a little girl. I remembered that, so I allowed myself to hope... perhaps I wanted to... we all deceive ourselves, when we want to believe. Melisandre most of all, I think.

I know this is very old, however I wanted to share this. Originally posted to my fb page.

Azor Ahai reborn

According to prophecy Azor Ahai is to be reborn again "after a long summer when the stars bleed and the cold breath of darkness falls heavy on the world".

We also have Melisandre saying this to Jon "When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt to wake dragons out of stone."
Jon has heard all this before from her and reminds her that "Stannis was not born on Dragonstone".

The Red comet: appeared in the sky over Westeros in 299AC. The comet's Dothraki name is "bleeding star". "Daenerys Targaryen first sees it on the night she had burned Khal Drogo, the night her dragons had awakened"

Daenerys:

• Reborn after a long summer ✔




• When the stars bleed ✔




• And the cold breath of darkness falls heavy on the world ✔ (the others coming back)




• Be born again amidst smoke ✔ and salt (Dragonstone?)




• To wake dragons out of stone ✔

As the post says, she not only sacrificed herself she also sacrificed Khal(King) Drogo and their stillborn son.

What Aemon thought: "Daenerys is the one, born amidst salt and smoke. The dragons prove it."
What Samwell heard: “Maester Aemon believed that Daenerys Targaryen was the fulfillment of a prophecy … her, not Stannis, nor Prince Rhaegar, nor the princeling whose head was dashed against the wall.”

In his youth Rhaegar thought he was the Prince that was promised, later Maester Aemon convinced him that Aegon was TPTWP because "for a comet had been seen above King’s Landing on the night Aegon was conceived, and Rhaegar was certain the bleeding star had to be a comet."
While in the house of the undying Daenerys, without having a clue about this, sees a vision of Rhaegar speaking about his son Aegon "He is the prince that was promised, and his is the song of ice and fire" and looking at her eyes while saying this.

More of Aemon:
"No one ever looked for a girl..It was a prince that was promised, not a princess. Rhaegar I thought … the smoke was from the fire that devoured Summerhall on the day of his birth, the salt from the tears shed for those who died. [...] What fools we were, who thought ourselves so wise! The error crept in from the translation. Dragons are neither male nor female, Barth saw the truth of that, but now one and now the other, as changeable as flame. The language misled us all for a thousand years."

Melisandre herself admits that she makes mistakes reading the fires, interpreting the images she sees wrongly. Mild spoiler for A Dance With Dragons

Mel gets her own POV chapters in A Dance With Dragons, and we finally get inside her head. She really does believe in what she says, and seems to be ignorant of Dany's existence.