Dye stamps only work on costumes. Outfits are free to dye at any dye station.
Dye stamps exist to get money from people who don't realize they can dye their costumes with ESO+ for free, or for those people who want to dye their costumes but don't have ESO+. Best thing to do if you don't have a sub is just wait for a free ESO+ trial and dye all your costumes then.
There are a few seasonal dye stamps that are really brightly colored, however... it would be nice to be able to either apply these colors to your outfits or unlock a real dye color. :-/
If you like one of the colors from those, you can dye a costume and then put different colors over the areas you want to change using the dye station. I've done that a few times. Like the bright red from the free level-up dye stamp is pretty nice, and I used that on a costume and then changed the two other ugly colors to something better.
Even if you don't like the whole palette in a dye stamp, sometimes one of the colors is a lot more brilliant than real dyes. So it might be good to at least preview them on different costumes to see if any of the colors looks nicer than what you have.
Just keep in mind that it's a one time only dye. If you change it later on, you won't be able to get it back. Why they don't just add those to your dye station colors is beyond me. Oh wait. Because someone actually spent some crowns. What I really don't understand is that people would probably throw a lot more money at them if they sold actual dyes instead of just dye stamps in the crown store.