The colors that FFXI selects for a new character? Might be easiest to do just that: make a new guy and see what you get. Alternatively, load up your character on a new computer or some place without existing local settings saved.
The picture you posted is from Battlemod. Can download the addon with Windower, load it up, and then type
//battlemod colortest to see all your current color settings. Note that the numbers you see (and the colors used in Windower's add_to_chat function) aren't RBG color codes or anything like that, but rather the number associated with a message type. 001 is for Say, 002 is for Shout, 003 for Yell, whatnot.
You can find out what color any given text message uses by making an addon with this in it:
Code
windower.register_event('incoming text', function(original,modified,color)
print('COLOR: '..color,'TEXT: '..original)
end)
It'll also print out color-changing characters used for things like items and key items, which go in the string itself.