It works pretty much the same as the weapon textures you were doing. Logos are stored in all the log_* files in pegs.vpp_pc and textures.vpp_pc.
ui_cl_logos.* is the tilesheet that contains the thumbnails that show up at the store when you browse them.
GotR has a ton of logos included that you can look at to see an example of the RGB values and how they work. For example:
0,255,255 - teal - transparent
255,255,0 - yellow - colorable
255,0,0 - red - black
The further you move away from those RGB values, the less pronounced the effect will be. For example, a muddier yellow, say, 218,220,40 will still take on the color you select from the grid in-game, but it will not be as bright as 255,255,0. For a more subtle black you would want to move away from a pure red to something like 201,56,56. I would also recommend doing very thin drop shadow outlines for your logos which will make it look crisper on the clothing and give it more pop.