The Appearance Vendor is located in the Base of Operations.
After collecting enough materials for the Base of Operations, wings will start to let you upgrade them. One of those, in the 
Security Wing, is the Supply Line. Once this upgrade has been installed, a vendor will appear in the back of the area. This vendor, called the Appearance Vendor will sell weapon skins and clothing/apparel. These items are randomly generated and reset every 24 hours.