I'm actually a OCG Fire King player, but i'll give it a try for the TCG. Ok, here is what you need to do in my opinion.
Fire King High Avatar Garunix - Since Yaksha isn't TCG, always run 3 of these
Fire King Avatar Barong - Always run 3
Fire King Kirin - Never play this card! It was the worst of the Fire Kings. Run 0-1
Sacred Phoenix of Nephthys - This is not a good card to run triple for. I would only run 1 if I was you.
Flamvell Magican - Pretty cool. Run 2
Fire Dog - Run 3
Mandicore of Darkness - ehh I don't really know about this card that much. You look like your trying to combo it with Kirin? I would run 0
Goka the pyre of malice - I would run 3 of these.
Onslaught - Always run 3
Fire King circle - run 3
Rekindling - I would personally just run 2
Dark Hole - Staple
Duality - Run 1-2
MST - Run 1 or maybe even 2 if you want
Book of moon - Staple
Torrential Tribute - Run 2
Try putting in 2 Maxx "C"
Also try one of my tech cards Swift Scarecrow. Run 2 of these
Try investing in 3 Fire Formation - Tenki
Try 2 tech in Fire Fist -Bear and 1 Fire Fist gorilla
Try getting a Fire Formation tensu
For your side
2 D.D Crow
2 Effect Veiler
2 Shadow Imprisoning Mirror - Dark worlds
2 Royal Decree
2 Imperial Iron Wall
2 Overworked - For when you face Fire Fist.
2 Summon Limit - Stops deck that over extended with summons.
1 Forbidden Lance