iPod Touch would be a good solution to your points above:
Seamless playback - check. (I've actually got Dark Side Of The Moon on my iPhone right now and just checked the transitions. Perfect.)
FLAC can be converted to Apple Lossless quickly and with no loss of quality if you really want to burn that much storage space on your phone. (Unless you're using a quality outboard DAC I can't see it being worth the tradeoff. Coming out of the standard mini jack, you'd be hard pressed to tell the diff between lossless and a decent mp3/aac encoding.)
You got me on the ogg point, although there are App Store apps that will play ogg. I can't speak to their utility/value as I don't use ogg.
Price - no contract, obviously, and you get a very decent little device that does way more than just play music. I personally wouldn't bother with less than 32GB which is $299, so I guess that is on the high end, but as I said, it's way more than just an mp3 player.
Controls... touchscreen is a matter of taste I guess, although I do have a pair of earbuds with an iPod remote built in that lets me change volume/pause/skip songs.
Headphone amp... see my point above re high quality DAC. If that's something that matters to you you know what to do and the iPod would be the cheapest part of your hardware chain most likely.
