Charizard's signature move | Bulbagarden

Maybe there's no consensus because he doesn't have one.

Flamethrower is a move many Pokemon can learn and is a TM.

The criteria you give for Fire spin is ridiculous considering those cards originated from the games, and the fact Charizard featured fire spin doesn't mean anything significant, and fire spin was learned by all (or nearly all) the first generation fire families.

Fire Blast, again same issue as flame thrower, and if your criteria for fire spin was that it was prominently featured in a TCG, Fire Blast was Blaine's Magmar's signature move of choice.

Blast Burn, while it was introduced to be exclusive to the Kanto starters, already felt like a "starter-exclusive" move along with the other elemental hyperbeams. The issue with that at the time though, was that it was a FrLg move tutor, and one of the criteria was that the Pokemon needed to be the player's starter.

It's not even the same case as that of Lucario's Aura Sphere which is still highly associated with it, and almost exclusively learned by it, and a few other Pokemon that have some sort of 'aura' feel (strong relations to emotions in Togekiss' case, and in Mienshao, sharpening its physical body with their mind) or are just legendary. Even the legendaries are exclusive in that they are either Mew and its clone, or one of the Sinnoh Dragon legends.

Same for Arcanine's Extreme Speed. Even now, the only Pokemon who learn it that aren't legendary, is a Pokemon that can enhance its body with aura, another Pokemon with debatable aura abilities (Togekiss' ability of empathy, and use of Aura Sphere) and a line of Dratini that is bred from a Dratini from a Dragon user clan whose most prominent member had game-defying Dragonites.

There's nothing really special or exclusionary about Charizard's moves. Most exclusives were in fact exclusive to those Pokemon until the introduction of a new game. Charizard doesn't really fit any of that.

The poll should really give an option of "none" as "other" implies that we think there is one

Personally, my vote would be Flamethrower, due to frequent usage in the anime as well as confirmation by SSB.

So we're going with noncanon material now? If I recall, a lot of the moves learned by Ness and Lucas aren't even stuff they know in-games. By that same token of logic, one can argue Fire Blast, or in the case of squirtle, Rapid Spin, as we've seen Squirtle do that in the anime long before it was an actual move.