From Gamer Escape's FFXIV Wiki, the free Final Fantasy XIV encyclopedia
|Dyeing an item is the process of using a dye to grant it a certain color. Dye can be crafted, purchased at vendors in the main city-states, or purchased from beast tribe vendors at higher reputations. Rarer dyes can be gained through Quick Explorations.
Most crafted gear can be dyed, but many gear pieces acquired in dungeons and duties cannot be. There is no limit to how many times an item can be dyed. Dye can also be removed by using a Terebinth.
Similarly, if you wish to paint a housing fixture or furnishing, you can do so by selecting Dye by accessing Housing within the Social menu. Alternately, furnishings can be painted when selected from the inventory.