I think the FM are trying to hatch their own dragon. The Citadel is rumored to have lore on dragons hidden away. We also know that Euron contracted the FM to get rid of Balon. We know the FM charge a huge price. Euron mentioned that he found a dragon egg(which is incredibly rare and expensive) and tied to hatch it, but that he later threw it in the sea in a fit of rage. He's probably lying though. Chances are that he used the egg to pay for having Balon killed.
Since the FM are probably aware of Dany and her dragons, my guess is that they are trying to hatch their own dragons as a counter measure.
Euron been in Essos for a minute and has amassed a lot of riches (supposedly a dragon's egg amongst other things). The fact that he came back to Pyke so soon after Balon's death (who had exiled him) is too much of a coincidence, and it suggests that he knew some shyt was finna go down. Add to the fact that Balon's death is mysterious as hell ---> Euron hiring a Faceless Man is a real possibilty.
Also peep the Ghost of High Heart's vision : "I dreamt of a man without a face, waiting on a bridge that swayed and swung. On his shoulder perched a drowned crow with seaweed hanging from his wings."
Like I said, Euron hired them to get rid of Balon and he probably paid them with a dragon egg.
We know Balon died while falling off a rope bridge that connected two of Pyke's towers, during a storm. The Faceless Men specialize in murders that seem like accidents. Then Euron shows up exactly a day after Balon died even though he was supposed to be exiled. That's some coincidence.
Then in one of Arya's chapters with the Brotherhood she meets the "Ghost of High Heart", a very old women who has prophetic dreams. She predicted the Red Wedding, Catelyn's ressurection, Renly's assassination, and Arya joining the FM herself.
She says
So a FM did Balon and Euron showed up the next day.
Then in AFFC Euron tells Victarion that he had a dragon egg and unsuccesfully tried to hatch it.
Could be that Euron just made the dragon egg story up, but we know the FM charge huge prices for a kill. That, and the fact that they are anti-Valyrian(peep the story the Kindly Man tells Arya), coupled with the fact that Jaqen is infiltrating the Citadel(where dragon lore is said to be hidden) suggests that he paid them with the egg and they are now looking for info on how to hatch it.
just when i think im figuring most of the shyt out, some other shyt comes around and blows my mind
i love westeros