"Flamvell" (フレムベル Furemuberu) is an archetype of FIRE monsters whose effects include burning away the opponent's LP and increasing each others' ATK. Many of their effects are triggered when they inflict Battle damage or destroy a monster as a result of battle and a lot of the monsters have 200 DEF or effects supporting monsters with this value. They are introduced in Duel Terminal - Synchro Awakening!! with further support in Duel Terminal - Invasion of Worms!!. They are introduced to the TCG through the Booster Pack Ancient Prophecy, with "Flamvell Commando" as a TCG-exclusive, with further cards coming through the Booster Pack Hidden Arsenal and Dark Neostorm.
The Japanese name of this archetype could derive from "flamberge". It is interpreted as "Fire Bell" in the French version, and "Flame Prison" in the Chinese version (or perhaps more properly, "Flame Hell", from the word for "hell" that literally means "earthly prison").
A Deck using the "Flamvell" archetype will try to overpower the opponent with monsters and, supporting this strategy, increases ATK values and inflicts burn damage. "Neo Flamvell" stay true to this overall idea while adding Graveyard-banishing effects to the party. The deck is essentially using FIRE monsters; Most of these FIRE monsters have 200 (or less) DEF and the archetype has effects to work with this small amount of defense. Furthermore, up to this day FIRE monsters from completely unrelated archetypes do have exactly 200 DEF to work with cards from back when "Flamvell" came out.
The "Flamvell" trump card is "Rekindling": It can get you up to five monsters at once, working similarly to "Soul Charge", but only for FIRE monsters and without the drawbacks. "Rekindling" can lead to various Synchro Summons/Link Summons or simply allows to run over the opponent with the monsters summoned this way. If the second option is desired "Flamvell Archer" can further increase the damage via its effect.
Unfortunately, both time and Master Rule 4 weren't nice to the "Flamvell" archetype. "Rekindling", unquestionably the main playmaker in the "Flamvell" deck, is Limited, making deck-building just that much harder. The aforementioned "Soul Charge" can be used as an alternative, but not being able to attack the opponent in the same turn really hurts the tempo and therefore the overall strategy. The usefulness of the other cards also dropped with the general power creep in the game; "Flamvell Magician" was one of the first Level 4 tuners, but has little to nothing to offer nowadays; the "Flamvell" player will still be forced to play him if he wants a searchable Level 4 FIRE Tuner due to the lack of other options. "Flamvell Poun" might have a big search pool, but needs to be destroyed by battle to trigger the searching and cards like "Flamvell Grunika", "Flamvell Fiend" or "Flamvell Commando" just are not impactful enough to make running them worthwhile. Even their boss monsters "Flamvell Uruquizas" and "Ancient Flamvell Deity" got victim to power creep and probably have to make way for other monsters in the "Flamvell" Extra Deck.
Regarding Master Rule 4, "Flamvell" was a useful archetype for Synchro Summoning back around 2010, but the advent of Link Monsters made them that much harder to use. Aside from "Rekindling", "Flamvells" really are not the best swarming archetype available and really lack options to place multiple monsters on the board without outside support.
"Red Resonator" is an absolute godsend in this deck. Normal Summon it and Special Summon whatever is available right after it. This allows the player to summon a Link 2, like "Duelittle Chimera" or "Crystron Needlefiber" (once it is available in the TCG), or go into a Synchro Summon of a monster with level 3 - 6. Special Summon "Flamvell Firedog" and try to destroy an opponents monster and you can go for even higher Synchros in Main Phase 2. "Red Resonator" also heals if revived via "Rekindling".
"Resonator Call" can be used to increase the access to plays via "Red Resonator".
Any Link Monster can help this deck to get field presence. "Duelittle Chimera" is helpful because of its effects, but basically any Link 2 will help "Flamvells", especially if the player still wants to use cards like "Formula Synchron".
"One for One" benefits this deck in two ways: The discard effect functions as Graveyard setup and the Special Summon can fetch an array of monsters like "Flamvell Baby", "Flamvell Poun" or "Flamvell Guard".
"Reasoning" can help the "Flamvell" player with the board building and gives extra Life Points when "Red Resonator" is summoned; these are not substancial, but anything helps.
"Cataclysmic Scorching Sunburner" can be used with relative success in a "Flamvell" deck. When summoned, it helps the Aggro strategy by being a relatively big beater, it has the potential to deal burn damage and it can even be summoned in the Battle Phase via "Flamvell Firedog" since it is a 200 DEF FIRE monster.
"Brionac, Dragon of the Ice Barrier" is an especially useful Synchro Monster for this deck: It helps clearing the field of potential threats while setting up the own Graveyard for "Royal Firestorm Guards" or "Rekindling".
Volcanic Flamvell uses the "Flamvell" cards summon useful Synchro Monsters (and at times Link and Xyz Monsters) and the Volcanics and their "Blaze Accelerator" is able to get rid of your opponent's monsters.
This Deck's strategy is to mix "Flamvells" with Zombie monsters, since some of the most beneficial Zombie monsters in the game share 200 DEF, the same as a majority of "Flamvell" monsters. "Flamvell Poun" makes an excellent search card because of that, netting the player either one of the "Flamvell" monster, "Necroworld Banshee", "Red Resonator" or a "Plaguespreader Zombie". "Flamvell Firedog" can summon "Shiranui Solitaire" upon destroying a monster in battle and allows the player to go through the basic Zombie summoning with "Mezuki" and "Uni-Zombie".
Since "Rekindling" and "Flamvell Firedog" play a large part in most "Flamvell" Decks, cards like "Vanity's Ruler", "Vanity's Emptiness", "Archlord Kristya" and "Fossil Dyna Pachycephalo" kills this deck type. In addition to that any deck with "Macro Cosmos", "Banisher of the Light", "Masked Hero Dark Law", "Dimensional Fissure" or similar effects will destroy the strategy by making it impossible to use "Rekindling"'s effect to its maximum extent, if at all. "Prohibition" or "Armageddon Designator" (the latter in Mirror Matches) can also prevent the use of "Rekindling", making it much harder to win. "Necrovalley", "The End of Anubis" and "Silent Graveyard" can also stop "Rekindling".
Any form of negation can also bring the "Flamvell" archetype to a screeching halt. They already struggle with filling the board to begin with and disallowing them from performing their already limited pool of plays can bring swift demise to the "Flamvell" deck.
"Blackwing - Jin the Rain Shadow" can destroy almost every "Flamvell" monster because a majority has a measly 200 DEF compared to "Jin's" 600 ATK. Many key "Flamvells" (i.e. "Firedog" and "Magician") are also Level 4, making them prey for "4-Starred Ladybug of Doom". By a similar token, "Water Dragon", "Star Boy" and possibly "Umi" can severely handicap "Flamvell" offenses.
Due to the "Flamvells" focus on Synchro Summoning especially, cards like "Discord" will stop them from getting board presence.