All code that depends only on the processor (i.e. paging, system calls, parts of the interrupt handling and of course those parts of Linux that were hand optimized by writing the code in assembler) has to be ported to Linux/m68k only once. This means that, with enough memory, the Amiga and the Atari may use the same kernel image. Another big bonus is that all user programs (= binaries) should work on any machine running Linux/m68k no matter whether the machine is an Amiga, Atari, Macintosh or VME system (or any future platform) as long as no machine-specific devices are used (see below).
All code that depends on the hardware is machine dependent and with very few exceptions which are in the kernel (timer, a small part of interrupt handling, startup code) has been put into modules called device drivers. Writing device drivers makes up most of the porting work.