Old thread but I figured out the above on my own.

The battery in my 2013 500 died. It was 4 years old, about as much as you can expect in Texas heat. I jump started the car and drove to the auto parts store. After jump starting the car, the EFI light was flashing and the check engine light was on, but everything was running normally. Put in the battery at the store and got the same result on startup: Flashing EFI light and solid Check Engine.

I drove the car home and before I got out, I tried cycling power several times without starting the car, then tried starting it again. The EFI light was fixed but still had the Check Engine light. I disconnected the battery for about 10 minutes, reconnected it and now everything is reset. I didn't tap the brakes or anything.