I think the firmware to use is the one in the first post of the firmware thread:
https://dashcamtalk.com/forum/threads/a129-pro-firmware.40465/post-484438
Not sure that is the very latest available, but as far as I know it is the latest reliable one, and I don't think there have been any recent updates due to an SDK update being in progress and taking some time.
When you say that your camera reboots several times during startup, does it fully reboot, or just restart recording?
The screen flicker is definitely a sign that there is not enough voltage reaching the camera, which means either a power cable of insufficient quality, or a power adaptor giving out insufficient voltage, or both. The fact that an alternative, non A129 Pro power adaptor also causes screen flicker is not a big surprise, some will cause flicker, some will work OK. It might be interesting to connect the camera to the power adaptor using an alternative cable, even if it is only a short cable for testing, but it does need to be a power/charging cable, not the data cable for connecting to a computer since that will not carry enough power to also power the rear camera.