During his chapters in AFFC, why does Aeron Greyjoy (the Damphair) have recurring memories and nightmares of a door with screeching iron hinges?
There is no canonical answer that I know of, but a prevailing fan theory is that Euron, his brother, abused him. The iron hinges remind him of nighttime visits.
The hinges screaming seems to be related to his brother Euron coming in the night to visit him.
That man is dead. Aeron had drowned and been reborn from the sea, the god's own prophet. No mortal man could frighten him, no more than the darkness could . . . nor memories, the bones of the soul. The sound of a door opening, the scream of a rusted iron hinge. Euron has come again. It did not matter. He was the Damphair priest, beloved of the god.
A Feast for Crows, The Prophet
The mutes and mongrels from the Silence threw open Euron's chests and spilled out his gifts before the captains and the kings. Then it was Hotho Harlaw the priest heard, as he filled his hands with gold. Gorold Goodbrother shouted out as well, and Erik Anvil-Breaker. "EURON! EURON! EURON!" The cry swelled, became a roar. "EURON! EURON! CROW'S EYE! EURON KING!" It rolled up Nagga's hill, like the Storm God rattling the clouds. "EURON! EURON! EURON! EURON! EURON! EURON!"
Even a priest may doubt. Even a prophet may know terror. Aeron Damphair reached within himself for his god and discovered only silence. As a thousand voices shouted out his brother's name, all he could hear was the scream of a rusted iron hinge.
A Feast for Crows, The Drowned Man
There's nothing beyond this to tell us what the hinge represents apart from him being scared of Euron. A fan theory is that Euron molested him as a child but as of yet nothing has been revealed. For more information on the theory see this A Forum of Ice and Fire post which has people arguing on either side of the fence.