Mine did the same thing a few days after I had been working on the car and had the battery disconnected for the work. Although the cables seemed tight, once they were reseated and tightened again, the problem never re-occurred, and I have not had to replace the battery either.
I think the flashing headlights and clicking sound part really indicates that your burglar alarm should be going off. I'll bet you'll say your alarm never works at all. That's the way mine was also.

It's kind of dumb when you think about it. The remote won't open the doors, so you use the key to unlock the door. Then you use the key to try to start the car.
I think at that point, because of a battery/low voltage issue, the skreem must not authenticate correctly with the remote in the ignition, and it assumes you must be stealing the car (ignoring that you used a key to unlock two locks).
That disables the starting function, and sets off the alarm on the car. Perfectly logical, but completely stupid.

And if you don't know about this tip, you get to pay for a towing bill, trip to a car repair shop, and a repair bill, maybe to replace a battery that just needed the cables tightened.

Worst part for me was, it was cold freezing rain, I had tools under the carpet in the hatch area, but since the power unlock was not working, I couldn't open the hatch to get to the tools.
I had to work my arms over the bulkhead wall behind the seats, which incidentally seems to be thick enough to be an exact replica of a bulkhead from the Titanic.
I keep a wrench in my center console now, waiting in case that happens again.

Since then I have put in a new Mercedes alarm that will make soft beeps when you lock and unlock the car. That way, the next time, I'll also have a blaring alarm to go along with the flashing lights.