The Lord of Dodona

Question: Why does Zeus have Prophecy associated?

Because Zeus is a god with a giant prophetic cult in his honor! Check this out:

This is the theatre of the Oracle of Dodona, once one of the most famous oracles in Greece, second only to the Oracle of Delphi in importance to the ancient Greeks. Where Apollo was the oracular power behind Delphi, dispensing visions of the future to its famous prophetess, Zeus was the power of Dodona, and granted to his priests visions and portents of the future through visions, the movement of his sacred oak trees, and the practice of augury based on the flight of birds. His oracle was the oldest in Greece, said by several Greek writers to be the first place prophecies were ever given in the land, and was visited by people from all over the ancient world, who came for the god's revelations of the future and predictions about what they should do next. The oracle is most famously mentioned in Greek myth in the Argonautica, where the prophetic powers of the Argo itself are attributed to the fact that it was built with a splinter of wood from the prophetic tree of Dodona.

Basically, he has Prophecy for the same reason that Apollo does. Several Greek gods had prophetic cults, but few as powerful and iconic as the oracles of Dodona and Delphi. Those oracles' powers were believed to come straight from their patron gods themselves, who were sometimes said to actually physically go to the seat of their oracle and at other times merely to send them the visions they dispensed to their seekers. The words of the oracle are directly the words of the god who inspired them, so it is Zeus who gives the prophecies at Dodona, from his own oracular powers. Dodona wasn't his only oracle, either, although it was by far his most famous one.

We don't always give a god an association based purely on cult worship, but in this case, the cult was so strong and influential, and it was so firmly based on the idea of the god himself having that power, that it was totally an easy choice for us. Zeus is a prophetic god with one of the most famous and influential oracles of the ancient world, and strongly associated with other prophecies besides, and that's good enough for us!