Yep, use the 0/12v signal from the flasher to control a charge/discharge. The ref voltage is simply a bypassed R-divider -- easy (and it would track your charge/discharge). It's been a while since I've had to look at the App Notes for the 3914, but my memory says that they had a lot of good info that would be applicable here...
You're right on the voltage range of these devices BUT... you're gonna need some protection circuitry for the hellacious transients that occurr in a car environment. (See comment below.) Linear regulators are pretty robust so in terms of component count and BOM cost, it's a wash as to the choice here.
Like I said, I'm certain someone can make this approach work. I wouldn't chose this method.
Reading through the automotive requirements that an IC has to withstand makes me chicken to use any kind of clocked circuit. Analog circuits are self-correcting when it comes to noise spikes whereas digital circuits get fatally confused.
But then again, I'm an analog guy -- what do you expect me to say?