This is my take at building a "Hazy Flame" deck. They piqued my interest during the "Create-a-card" contest Konami is still holding at the time of writing this. The archetype, unfortunately, did not manage to get out of the first round, but it certainly sparked some interest in people. "Hazy Flame" is an archetype that consists entirely of Level 6 Fire monster with their unique shared effect being that they all cannot be targeted by the opposing card effects. The goal is to summon multiple of those Level 6 monsters to summon various Rank 6 Xyz monsters and win the game using the effects of your assembled Extra Deck force.
The combination of needing both Level 6 and the Fire Attribute is fairly restrictive, meaning that you will have to stay in the archetype to gain access the Extra Deck. But thankfully, there are some options to work with on that end. "Hazy Flame Peryton" is your main playstarter and can be Normal summoned via "Hazy Pillar" without tribute, who can Special summon two "Hazy Flames" by tributing itself and discarding another Fire monster. This allows you to search for any combination of "Hazy Flame" monsters, but an especially useful combo is picking double "Hazy Flame Hydra", which locks you into summoning Fire monsters but not only can be used to summon the very powerful "Evolzar Solda", but also give whatever monster you Xyz summon using them additional Xyz materials from the graveyard (which you already setup via the effect of "Hazy Flame Peryton").
"Hazy Flame Griffin" can be Special summoned from the hand if your opponent controls a monster and if everything in your graveyard and on your board is Fire Attribute, but can also be cheated out via "Fire King Island". "Hazy Flame Cerbereus" has a handy effect to Normal summon itself without tribute and is your main searcher in the deck who is triggered by being destroyed; something that both "Fire King Island" and "Goka, the Pyre of Malice" happily do for it. "Fire King Island" can even destroy it in hand and therefore allows you to access the first combo I named without losing the Normal Summon slot to "Hazy Flame Cerbereus". "Hazy Flame Sphynx" has no summon help itself, but can potentially fetch a monster by guessing the top card of your deck correctly (since the deck is mostly monsters, I would suggest guessing that most of the time).
Further summoning options in the deck are "Rekindling", since "Hazy Flame Hydra", "Hazy Flame Cerbereus" and "Hazy Flame Hyppogrif" have 200 DEF. This is also the only reason why "Hazy Flame Hyppogrif" is in the deck at one copy. "Fire King Arvata" is the searchable card for "Fire King Island" and provides effect negation in addition to being a more summonable monster if you cannot access anything else. "Evoltile Megachirella" might seem weird, but it can trade itself against "Hazy Flame Hydra" with relative ease while also potentially refueling "Evolzar Solda". "Hieratic Dragon of Tefnuit" is not a Fire monster, but can Special summon itself if the opponent controls a monster and also fetches the single copy of "Tyhone #2" when being used as tribute, which together with "Hazy Flame Peryton" and "Hazy Flame Hydra" could summon your boss monster at maximum power with five materials.
The backrow was mostly mentioned already: "Fire King Island" and "Hazy Pillar" are there for consistency reasons, while "Rekindling" not only has the task of providing Xyz material but also could accrue a full board of ~2000 ATK monster, which can be used for a surprising beatdown strategy. "One for One" searches for "Evoltile Megachirella" (albeit this way of accessing "Hazy Flame Hydra" will cost quite a few hand cards), "Monster Reborn" is the usual graveyard summoning tool while "Foolish Burial" allows for graveyard setup. The two "Hieratic Seal of Convocation" allow for the search of "Hieratic Dragon of Tefnuit" and further boost the otherwise weak consistency and "Celestial Observatory" can add copies of "Hazy Flame Hydra" or other monsters you potentially do not need in the hand to the deck and refreshes your hand.
Since I already mentioned the boss monster: "Hazy Flame Basiltrice" was (and still is) the main goal to summon in "Hazy Flame". This fiery chicken has sizeable stats, a banish effect and added protection at five materials, but sadly dies rather easily to "Kaijus". Other than that, the Extra Deck is filled with a variety of options to go into in certain situations: "Number 39: Utopia Beyond" supports the beatdown strategy by lowering the opposing monster line-up to zero attack, "Constellar Ptolemy M7" bounces monsters you can not destroy, "Photon Strike Bounzer" is a potential turn one play which can block opposing monster effects, "Number 6: Chronomaly Atlantis" is just a beatstick, "Jinzo - Layered" is a "Crackdown" on legs and therefore steals opposing monsters/defenses and "Fairy Knight Ingunar" bounces the entire field except himself. "Evolzar Solda" was already mentioned, but it is probably the best control option you can get on the field turn one and, since you normally use "Hazy Flame Hydra" to summon it, will have four materials attached to it instead of the usual two. The Link options mostly stay untouched, but "Duelittle Chimera" can be useful for the aforementioned "Rekindling" beatdown while they all serve as easy options to go into if you do not have any better options to go into with the "Rekindling" resources (since those monsters are banished at the end of the turn).
So much for the strategy. I have to add that "Hazy Flame" is pretty bricky due to the usage of Level 6 monsters and being without any good Attribute support cards to boost their consistency (since Fire does not provide much helpful generic support). The deck can be stopped with relative ease if the opponent can throw a negate into your plays and there will be times in which your starting hand does not provide any playable solutions at all. Also, the archetype has problems with doing anything other than putting some Xyz monsters on the field (not unlike the "Battleguards", which do essentially the same but with Rank 5 Xyz). All of these things are good reasons for Konami to re-visit the archetype in the future with some support.
If you are interested to read more about the "Hazy Flame" archetype (or various other archetypes), feel free to visit my blog via the link here: https://cubiccreativity.wordpress.com/2020/09/13/archetype-analysis-hazy-flame/