In order to use this, it must be traded to one of the NPCs that deal with Chocobo Racing and buying Chocobux items. They can be found wearing orange vests and standing directly outside the Chocobo Circuit. This dye can only be used if you have a chocobo whistle and will only be applied to the chocobo currently on that whistle. This dye is temporary, per-say. The dye will stay on your chocobo and will make your chocobo appear the desired color every single time it is called to the field. It will NOT appear as that desired color when it is in the chocobo stables or when it is in the chocobo races. The dye will, however, "wash off" the chocobo when you change the chocobo on your whistle.
Edit: Also, when the stats on your chocobo change and you re-register the same chocobo to your whistle to update the stats, the color will wash off. I suggest not using the dye until you have the desired traits on your chocobo and you are ready to retire it.
hmmm the dye cost 50 chocobux and will affect the chocobo registered to your Chocobo Whistle. As soon as you change or update the choco on your whistle though, the dye will go away, or as they say in-game, "wash off". I think if you have 0 charges, and renew a whistle, that the dye will not go away. The dye should remain, as long as you don't reregister the same choco to update stats, or change the choco, but I'm not sure, haven't tried it.