My visa was refused — can I get a refund for the flight ticket I'd already bought?

No. Unless you chose a refundable fare, a refund is not possible. A visa is a document issued by a country's authorities allowing you to enter for the purpose stated in it, and holding a valid visa for your destination is the passenger's responsibility. Since neither the airline nor the ticketing agency is responsible for whether your visa is granted, they have no obligation to refund you. That said, it is still worth contacting the airline or your agency at least 3–4 days before the flight to discuss rebooking to a different route or converting the ticket into an open ticket.