Most people do not post them up -- people like sprite sheets and people like text dumps but they do not care so much for the intermediate files.
You get to find one in the game or rip it from a play of the game. Depending upon what you are doing one may be easier or more useful than the other.
I take it you understand the concept of paletted imaged but if not the quick rundown is game artwork usually uses a crude paint by numbers image where all the shapes are squares*.
*someone prepping to tell me about pixel aspect ratio, can we nod and say we did? Someone prepping to tell me about some of the more exotic referencing pixel colours, can we also nod and say we did?
The four main methods are
Get lucky
Works well on the DS where the tiny files named the same as the picture files and tile layout files are usually the palette. On the GBA it is usually a good bet you will find it near the
Savestate/emulator rip.
The palette is loaded into memory (it is how it works after all) so a savestate will contain it. You can rip it from the savestate for use in editing a tileset. Naturally you can not change the colours if you do just this but if you just want to change a few pixels using the existing colours (or rip it for a spritesheet or something) then it works great.
Savestate guided palette rip.
If you have the palette from the game from the above method you can try searching for it in the game. Works pretty often and if you are willing to narrow it down and search for a fragment then it can even dodge the dynamic palette issue.
ASM/tracing rip.
Emulators are advanced enough that you can tell them to tell you when certain things happen
Like
http://www.romhacking.net/documents/361/ but you are looking at the Color Palette RAM (05000000 through 050003FF hex) instead of the VRAM. Works well if you have a hidden one (buried in the game binary rather than as standalone data) or a dynamic one.
My usual go to GBA tile editor of
http://home.arcor.de/minako.aino/TilEd2002/ can pull it from savestates as well.
Main problems additional to the problems with paletted images themselves
Compression (not common as palettes are small and do not go into vram or wram like most other data)
Dynamic palettes. It is a common animation method to cycle colours at palette level (my two favourite examples on the GBA are the save swords of summon night 2 and the rainbow blocks of Mr Driller). This is mainly an issue if you are searching for it from the palette as above or having to change the colours you can use if it would effectively deny you a few of them. Dynamic palette does also extend to brightness/darkness options (again summon night 2 being a good example of a game with such a technique though many more got original GBA and SP options).
Shared/reused palettes. A game might reuse a palette for something else so if you change it then it breaks something else.