Melisandre, a worshiper of R'hllor has stated that,
“When the red star bleeds and the darkness gathers, Azor Ahai shall be born again amidst smoke and salt. ”
Much later in Braavos, when talking of the prince to Samwell Tarly,
Maester Aemon mentions smoke and salt as being part of the heralding of the prince that was promised coming. Maester Aemon was aware of Rhaegar's beliefs, though it is unclear if he shared them. Aemon would later came to doubt the wisdom of looking for a prince, rather than a princess. He realized there was a translation error, and that the term translated was fluid in terms of gender. This is connected to the term for dragons, which are neither male nor female.
The mention of smoke and salt brings to mind Melisandre’s above mentioned statement. However, Tyrion Lannister has stated that:
“Prophecy is like a half-trained mule. It looks as though it might be useful, but the moment you trust in it, it kicks you in the head.”
Azor Ahai and the prince that was promised may be two distinct prophecies, or they may be one in the same in a prophecy that has the potential to turn out to be about two separate people. The prince may not even be male; the prince may have been referred to as male erroneously for centuries. Aemon firmly believes that the prince is not a prince but a princess, as High Valyrian is a language in which nouns are gender neutral.
Aemon also says to Samwell that the dragon must have three heads. He wakes up weeping, wailing:
“ The dragon must have three heads … but I am too old to be one of them. I should be with her, showing her the way, but my body has betrayed me. ”
It may be that the three-headed dragon is a part of the prince that was promised prophecy, and there are two other people whom the prince will need to have by his side to show him the way.