At some point between How to Train Your Dragon 2 and the third movie (a span of about a year), Fishlegs' armor was constructed.
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Fishlegs' dragon scale armor appears to be formed of several different pieces tailored to fit his body. There is the helmet, pauldrons/should piece, chest plate of sorts with a carry pouch, a skirt-like part over the hips and leg, gloves and gauntlets, arm pieces, and boots. There are also two wing structures kept folded for flight when needed. The suit is made out of Meatlug's shed scales, so has a predominantly brown color. The scales appear to be attached to a leather base, with presumably Toothless' sticky saliva as the gluing agent. The whole suit is further embellished with thick metal balls, mimicking those of Meatlug.
Due to its construction from Meatlug's scales, Fishlegs' dragon scale armor is effectively impervious to fire. It is unknown if the non-scale portions are also treated in some way to be fire-retardant.
As a suit of armor, it affords some protection from attack, much better than normal clothing. However, dragon skin and scales can be cut and pierced, so the armor is not fully protective from all attack.
Fishlegs has incorporated a basket-like pouch on the chest of his suit, exclusively to transport a baby of Meatlug's, named Fishmeat. The tiny tooth is able to be transported with some degree of protection.