Aemon talking about Daenerys-plot hole?

[Rhaenys' kitten]

This is a bit of a plot hole I've noticed. Aemon and Sam now know about Daenerys and her dragons. Yet somehow they must not have shared this information with Stannis and Melisandre.

Stannis's entire claim to the throne is that it is his by right. Claiming the IT is his duty, and Stannis is nothing if not dutiful. So why wouldn't he at least discuss/contemplate whether he ought to declare fealty to Daenerys?

And even if Stan didn't do anything with the information, it would have to have huge significance for Melisandre, that there are dragons in the world again, and a princess born amidst salt and smoke.

In the books,

Aemon doesn't learn about Daenerys until Braavos

,

so this is a show-only plot hole.