Are there any Dye with Special effects?
Any effects (like shine or reflective properties) usually has more to do with the material being dyed than the dye itself, honestly.
Yes, it depends mostly on material. But the “shiny” effect is more noticeable when applying metallic dyes to metal armor, and natural leather dyes sometimes give leather parts of the armor a more pronounced texture.
Other than that, there aren’t any effects of note.
There’s nothing that’s really over the top in terms of being shiny or sparkly, but some dyes are particularly bright (Acid is a good example). There are also some dyes that have a bit more of a special texture on armor. Check out the Enameled dyes, like Enameled Crimson for this.