I'm not sure if you're still working on this because of the last post date, but I've got some answers:
You won't need any kind of video amp, the Flashback 2 outputs a strong enough signal for standard lcds to use. You will need an audio amp however, since there aren't any good small screens with audio built in. I'd suggest building this: viewtopic.php?f=9&t=1231
. As for batteries, my suggestion is to use two 18650 lithium cells. They're 18 mm thick, and the SL-64p has 23 mm of inside depth. A 3.5 inch screen, audio amp, and Flashback 2 have hardly any power consumption. At 7.4v, it'd be something like 500 mah, if not a lil bit lower.
If you don't do it, I might, since nobody ever bought that Flashback 2 off of me.