Other than other User Shops, the only place you can option Dye Kits is the NPC Shop called the Black Market which you can find under the Shops Tab at the Top and on the NPC Shops page. It'll be the first image in the very last row of the man with Tu coins in the background.
You could also get a Random Dye Kit from Kir's Quest, which has a chance to change your pet to any of the Dye Kit colors.