24-bit DAC + D-class amplifier in singlechip - good solution for pocket MP3 player?
Your limiting factor is probably voltage swing.

If your driving higher end headphones your probably looking at a 250->300 ohm load, 300ohm for higher end sennheiser cans for instance.  But some phones (mostly professional models) can go as high as 600 ohms.

At 300ohms:

For 100mW you need 5.47 Vrms = 15.48 V peak-to-peak ( 18mA RMS)

For 200mW you need 7.75 Vrms = 22 V peak-to-peak ( 25mA RMS )

You probably won't find an integrated part that is specifically designed for portable devices that can achieve those levels of voltage swing.  Your best bet is probably an audio op-amp with a high drive current (TI makes several, as does analog devices) or a purpose built headphone driver, for instance the TPA6120A2 would fit your needs.  

Your challenge is then to build an efficient power supply to generate the +-12-15V rails needed.

Not sure what your plan it for batteries but one way to make it easier and more efficient is to use two batteries, maybe two 9V batteries, center tap for ground giving you +-9V rails to start with.  You end up with bigger/more batteries but you don't lose any power boost converting up to your + rail and then using a charge pump or similar to get your negative rail.

EDIT: I'd target 100mW MAX...200mW would explode your head with most phones.  expect 97-102db sensitivity at 1mW for most higher end cans (could be lower for pro models).  meaning at 127mW you'd be looking at SPL in roughly the 115dB to 120db range which is more than enough to cause hearing loss if listening for extended periods.  Targeting ~63mW would put you at 112db -> 117dB which eases your voltage swing constraints and can still cause plenty of ear damage.