Sounds cool!

Yes, the oracle of Delphi still existed during the Roman period (until the end of the 4th century).
But there were other sanctuary where oracles / priests / sibyls could make predictions. If you don't want to make your characters travel all the way to Greece to go Delphi, one famous oracle in Italy was the Sibyl of Cumae. If the gods exist and you characters go there, maybe it could even be implied that the woman they meet is the real mythical Sibyl?

I don't know what I'm gonna do for a prophecy thing yet. I'm still in the planning phase.

ok!^^ It was just an Idea. There are many way where you can get a prophecy, as in Roman time you could find someone who could read your futureliterally anywhere (from augurs studying the flight of birds, to astrologists or people who read the future in the bowels of animals). But yes, it will be easier to know which way fits the best once you know what the prophecy is about, but just remember that if you make your characters go to Delphi, they'll have to travel to Greece :).

Honestly, a quest to very far away might make more sense, since they're on the run for their lives.