It's one-use, and it's meant to be used on costumes (from the crown store or certain achievement or quest rewards) rather than on gear. You can preview it on whatever costumes you have in your collectibles, and then once you commit to using it, the costume will be dyed permanently in those colors (unless you re-dye it later).

You're probably talking about the dye stamp you get from leveling - the fact that it's a leveling reward is what makes it character-bound.

They tend to show up in the crown store as limited-time offers or around events. I think they've also been showing up in crown crates lately.

Since you asked about the outfit station too, keep in mind that you can dye your armor pieces for free (making sure you have "No Outfit" selected) or set up an outfit using whatever crafting styles and dyes you have available (which will cost gold). That's based on the dyes you've unlocked by getting associated achievements and the motifs and outfit style pages you've learned.