seeing the fanstastic little racial feat for the tiefling known as flames of phlegethos which lets you "call on hellfire to serve to serve your commands" and has an effect that is as awesome as the name and description letting you create an fire aura that hurts creatures who attacks you, that appears right after you cast an spell that deals fire damage, and combined with the green flame blade cantrip it can probably make for an really interesting melee build, but i am torn on what class is best for such an build

blood hunter order of the profane soul pact of the fiend really fits the edgelord aestetic and lets me have a fire sword at 2nd level and the cantrip at 3rd

eldrich knight fighter could work really nicely with the bonus feats and the reliance on getting hit for the feat to work counteracted by second wind a little

warlock pact of the blade and hexblade, fiend or even celestial could also work out nicely and then you get you get green flame blade early on, martial weapons, using potentially using charisma for both attack rolls and damage or add charisma to one damage roll of green flame blade

i am indeed very torn on this and any advide would be helpful

I would say blood hunter. Put 15 in dex, 14 in con, 13 in int, 12 wisdom, 10 charisma and 8 strength. Then like you said, fire for rite damage. Pick up a rapier. Either profane soul or ghostslayer. Ghostslayer for the ability to attack with radiant damage, and ethereal step.

Quote from KaoshiElder29 >>

I would say blood hunter. Put 15 in dex, 14 in con, 13 in int, 12 wisdom, 10 charisma and 8 strength. Then like you said, fire for rite damage. Pick up a rapier. Either profane soul or ghostslayer. Ghostslayer for the ability to attack with radiant damage, and ethereal step.

 why would i ever waste my time with dexterity, when i get to make one attack per turn and i need to get hit in the first place in order to trigger the feat, and i need to be able to cast green flame blade for the build to work? I was thinking more like a glaive or an greatsword to deal as much damage as possible with the few attacks per turn that i get. Also this build litterally cannot work if i cannot cast the cantrip in the first place, so what is the point of picking ghost slayer? and since i am already going with fire why pick a subclass that gives me another rite that is not fire? like the benefit of the fiend pact, something that also fits the aestetic of the tiefling who uses a lot of fire

i was thinking more 15 str, 15 int, 14 con, 10 charisma and 9 everything else, possibly going like zariel tiefling instead of default tiefling for +1 str and +1 int with the feat later on

Ok, just my thoughts. Radiant damage for when you face things with resistance to fire damage. Asking for ideas then scrutinizing them doesn't work well. If you already had the idea, then don't ask. Tell others without asking. I gave it high dex as I would use flames of phlethegos only if I got hit and took damage. If you want to get hit, go with either fighter or paladin. Then you can deal loads of damage and get hit without worrying. You asked for my build, I gave it. 

yes i asked for advice, but i asked specifically about an build that combines the green flame blade cantrip with the feat flames of phlegethos into some sort of melee build, that was the premise, and i was a little torn since all three seem to be able to do the thing really well, each had an diffrent advantage from the eldrich knights fighter's extra staying power and versatillity in evocation spells to the blood hunters peak aestetics and the hexblade's chance to not use anything that is not charisma, all of them can pull this off well and i wanted to know, of these three fantastic classes / subclasses / builds witch one is slightly better, and perhaps something i had missed or forgotten

All three of those options seem to fit the build nicely, with none having major advantages or disadvantages over the other.  One question that was already raised and is worth thinking about is how will you handle it when you're dealing with fire immune enemies?  

Celestial patron could work for that (if you still want green flame blade). 

Quote from Rav_Saadyah >>

All three of those options seem to fit the build nicely, with none having major advantages or disadvantages over the other.  One question that was already raised and is worth thinking about is how will you handle it when you're dealing with fire immune enemies?  

 *shrug* the blood hunter and the warlock could always use hex and rely on extra attacks, as could fighter, and there is an blood curse that lets you overcome resistance and immunity, the more i think about it the more i lean blood hunter and yeah i have already decided mostly. So if it is immune, i rely on hex and extra attack and greatsword, and eventiually an blood hunter does get other crimson rites with other damage types, as well as that i might also learn booming blade or eldrich blast as my second warlock cantrip, i am not helpess against fire immune creatures (but of course fire is where i would naturally excell)

Quote from KaoshiElder29 >>

Celestial patron could work for that (if you still want green flame blade). 

 agreed, with its bonus to fire damage it could work indeed rather fine in this context