Stability light keeps blinking

Those two codes are for the rear wheel speed sensors. As this problem all started at once the issue is not likely the sensors themselves but a wiring problem from the rear sensors, the wiring harness is a know problem area on them.
When any of the sensors drop out the system will disable the ABS system and as the stability and traction controls use the ABS system for operation they are also shut off and the warning lights come on.

I would start by visually checking the wiring from the sensors, if you have access to a good live data scan tool that can read the ABS system it would help.

It will flash because the stability system will keep trying to work but it then discovers there is a fault in the ABS (which is the system that the stability system controls to provide the stability) and switches back off. The light comes on and flashes to scream "I am not working, fix me now or suffer my wrath" Basically the systems are linked together so if one fails, they all shut down because they all work together.