If you have an empower-to-cigarett-lighter adapter, it's possible that it converts 15v to 12v before it even hits the cigarette lighter. I can't see them making it otherwise, unless it has a warning that says "Only plug a cigarett-lighting device in to this cigarette lighter."
Here's why I say this... Diodes are available that can handle many amps, and all it takes is diodes to step the voltage down from 15v to 12v. (specifically, four of them, or one 3v zener diode.)
The real trick will be in the power consumption. You might be ok if that cigarette lighter adapter uses diodes to step down, but if that DVD player takes a lot of juice to run then the adapters you're using have to suck up all of the excess power as the 15v is stepped down to 12v. (if all components are perfect, that's 20% of the total power consumed in the empower-->cigarette adapter and another 11% in the cigarette-->DVD one. Realistically, it's probably more like whatever power the DVD player consumes, 45% to 55% on top of that will be consumed by the adapters.)
So take the power requirement of the DVD player in watts, and multiply it by 1.5, and that's the power you'd pull from the plane. Make sure that the number you get is under the maximum power the plane will supply. Then, while the DVD player is on, constantly check those adapters to see if they are getting hot. I had a laptop plugged in to a car using a funky scheme like that, and it overheated. (had cigarette lighter --> power inverter --> laptop power plug w/ DC converter --> laptop. The inverter burned up and died after half an hour even though it was rated good enough to handle it.)
If nothing gets real hot and 150% of your DVD player's power requirement is still safe for the plane, you should be good to go.