Fire Dragon Armor is a set of four items which can be obtained by attackingMountains level 7 and higher (the higher the level, the greater the drop rate) with a Great or Elemental Dragon as part of the attack. Alternatively, they can be purchased from the shop. Once you have obtained all four pieces, have Outpost 3's Dragon Keep at level 8+, and have Aerial Combat at level 1+, you will be able to include the Fire Dragon in your attacks.

As the items have a small chance of being found on each attack, many attacks will likely be necessary to find the set. Researching Aerial Combat, upgrading to higher level Dragon's Keeps and unlocking other Elemental Dragons will reduce the minimum time between attacks.