As the items have a little 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.
Drop rates have been lowered for the fourth time to make the game more challenging for months of farming, and increase ruby purchases. Expect a lot of fruitless farming and frustration. Fire Dragon Armor is a set of four items which can be obtained by attacking Mountains level 7 and higher 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 Dragons Keep 8+, and have Aerial Combat at level 1+, you will be able to include the Fire Dragon in your attacks.