Well, as I'm not getting any kind of response to help with this issue I'll answer it myself.
Yes, it is possible to flash firmware to this board. If you get an ST-LINK programmer it is pretty straightforward.
I ended up getting the ST-LINK/V2 ISOL version. I believe any other version should work fine. With the isolated version, you will need to power the board from another source when programming.
Here's a picture of my setup. (The blue wire not connected is the tx pin of the debug uart on the board)
To create the cable, you will need to have the connector for the debug port, I just bought them from digikey along with some pre-crimped wires to make it easy. I then took the existing ST-LINK provided cables and soldered them onto my new wires; inserting those into the debug connector. Here's a closeup of my cable. Note that the pin at the top is pin 1.
Information about the pinout and the connector is available in the modai docs here.