i'll skip over the regular salamangreat plays because the deck can play like any regular salamangreat deck post promethean princess
instead i'll focus on explaining the FTK, it's not very complicated
the 2 cards you must fetch are salamangreat weasel and salamangreat sanctuary, besides that all you need is a way to summon salamangreat raging phoenix WITHOUT promethean princess and by using heatleo (IMPORTANT) to climb into it
let's go with a combo example, i used a random test hand because there's a ton of ways to do the combo so focusing in just one is pointless
the first thing you want to do is get the field spell with balelynx:
then, get 4 materials worth of link mat and at least 1 more summon, also have weasel in field or GY (or hand as the extra summon)
you must climb into raging phoenix using heatleo (in theory any link-3 fire that can be summoned from gy later works)
once you summon raging phoenix, summon it again by using its copy as mat to search will of the salamangreat and use its second effect
use 3 of the summoned monsters to link summon promethean princess, then use her effect to summon heatleo, you need to have weasel on the gy or field ready to be used as material for the next step and an extra level 4 or lower FIRE monster in the field
after this, summon salamangreat pyro phoenix by using either link-3 and raging phoenix (it's important to keep a level 4 or lower FIRE monster), then use weasel's effect to summon a raging phoenix to your opponent's side of the field and use pyro phoenix's effect to burn your opponent for -2800
here, use the extra summon and pyro phoenix to summon "hiita the fire charmer, ablaze", your field should have 1 level 4 or lower FIRE monster, hiita and one link-3 monster at this point
then from your deck (or hand) summon greater inari fire by tributing the level 4 or lower FIRE monster and hiita, use its on-summon effect to burn 2800 more LP (after that your opponent would be at 2400 LP)
then, link away greater inari fire and your link-3 to summon any link-4 with 2400+ original atk (for example, amblowhale), and use greater inari's second effect when sent to GY to search spiritual fire art - kurenai
set kurenai, pass turn and in the draw phase simply use kurenai by tributing your link-4, dealing the finishing blow to your opponent
and that's the FTK (technically it's not an FTK since it ends at the start of your opponent's turn, but there's not much your opponent can react with to win this situation)
only warning i'd give is, if you know your opponent is playing purrely skip the FTK as pretty memory will save their ass, also this FTK is very weak to interruption but as per usual with FTKs it's immune to blowouts, if you suspect your opponent could handtrap you i'd recommend simply skipping the FTK and going for a safer salamangreat board
the deck, in general, is also fine as a regular salamangreat deck since the FTK is very low-commitment in main deck and extra deck space (without counting cards that you'd regularly run in salamangreat, it's 2 main deck cards and 1 extra deck monster)
i recommend trying out test hands before giving it serious plays, so you can get a feel of various play lines needed to reach the FTK
have fun jumpscaring people with a surprise FTK if you try this
pointless note: i generally don't post my decks anywhere, but in this case this is a theorycraft that i've never seen anyone come up with (as far as i know, i could very easily be wrong and look like a tool), so i'm making this as an archive of "i made this first" proof, also i went 4-0 in a pre-realese test tournament with this and the FTK worked out quite a few times and the regular salamangreat pivot also worked so i feel confident enough in the fact that it's not 100% a meme