Looking at the documentation for the flight core v2 I see that is supports px4 and that there is planned support for ardupilot. Is there any kind of timeline for this support? Has any work on this begun at all?

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.

I just got my Flight Core v2, and I'm looking to do some software testing on it. One of the first things that I'd like to do is to run some flight software other than PX4, is there any option to load other firmware?

I see in the documentation that you can upload other PX4 firmware with the PX4 tool, and there is a mention of using the STLink v2 to flash firmware, but I'm not exactly sure what is needed. Do I need a special connector for the STLink? I haven't purchased one yet, but if all I need is to buy it then that's not a problem.

Alternatively, I know that the STM32 chips have the DFU mode. Is the BOOT0 pin exposed on the flight core so I can upload firmware directly over USB? If so, where is it located?

Looking at the documentation for the flight core v2 I see that is supports px4 and that there is planned support for ardupilot. Is there any kind of timeline for this support? Has any work on this begun at all?