Hi!
I am a programmer interested in embedded systems. I just read the ZSP400 datasheet and think a normal linux kernel for that mp4 is nearly impossible.
However, a custom build kernel targeting the architecture may run ok. The chip itself supports hardware multitasking, which is great.
The problem I can think of is the lack of a Memory Management Unit (MMU). Without this in the CPU, running user processess is almost impossible, because all programs share same memory layout, so a process may deliberately (or because it's buggy) trash other app memory or even kernel memory.
However, a minimal set of functions (to work with the screen, integrated dsp(for sound) , to work with the touch screen, operations from flash memory) may be implemented, creating an operating system as operative as DOS, where only one task can run simultaneously and that task can communicate with the kernel via interrupts or syscalls.
If after that you still want to use linux in your player, check uClinux.org and wiki.s1mp3.org . In s1mp3 page the staff is developing a replacement firmware for these players. Also there is
http://wiki.s1mp3.org/NanoComputer which has a simple operating system.
Cheers,
Gonzalo (from Argentina)