The most simplest of strategies, go second and blow-up the field! And keep blowing it up!
In addition to that, Fire Kings, in the beginning of a game at least, is reliant upon the normal summon (at least your traditional builds). The deck will eventually be able to spit out special summoned monsters after the first turn, but it needs set up. This is why this is not a "go first deck" most of the time. There are some "go-first" cards, but first turn openings are sub-par. This is why I have tinkered with the deck through the years, adding Fire Fist-Leopard (to search Fire Formations), a Fire Formation Tensu (extra normal summon), and Caninetaur (dump a monster in the graveyard). Now with the addition of Gizmek Yata, you are able to get an additional normal summon, plus a monster card in the graveyard for a special summon (note the restriction on the special summoned monster due to Gizmek Yata's effect).
I also included Naglfar, Generaider Boss of Fire into this build as a way to control the destruction ability of the High Avatar Garunix, plus give a level of protection against battle and card effects that you don't want to hamper your board (either through your opponents effects of your own). This in effect allows you to control your side of the field in a more pin-pointed way, and not just rely on blowing up the filed over and over. Which is still so fun! Plus, Naglfar is a level 9 beater that can be used with Agnimazud to bring out True King of all Calamities from you extra deck.
Please note than I am still trying to figure out the right ratios with these inclusions. Plus I would like to add some draw power to the deck, but not with Supply Squad seeing it can be a huge dead draw (personal experience).