A Rose by Any Other Name...
You want a flamethrower that isn't a flamethrower. Strictly speaking, that can't be done. The value of a flamethrower is that it can deliver combustion to an incombustible area. For example, a concrete bunker.
Could you do that with a tool that (ignoring electricity) remotely combusts things? No. Nothing inside the concrete bunker other than what was brought for the purpose of the bunker is combustible. If it's a machine gun nest, then the ammunition is combustible, but how would that be ignited by a remote heat generator? And if you could ignite it, you wouldn't be igniting all the ammunition at once but only that ammunition that fell under the "beam" of the weapon.
Worse, a remote heat generator of any sort (electric, laser gun, solar optics, etc.) can only work line-of-sight where a traditional flamethrower fills the space with combustible material.
Conclusion: Not viable
Flamethrowers don't just throw flame. They throw a burning substance. WWII flamethrowers used a stable substance like diesel fuel. If you pierced the tank with a bullet, it actually wouldn't explode. Have you ever tried to burn diesel fuel by just setting a match to it? I have. It takes forever to burn away. But convert it into a spray and it burns quite readily. Coat something with that spray and whatever is coated burns. Without the ability to coat something with a combustible material, you don't have weapon that solves the problem flamethrowers were invented to solve.
Note #1: piercing the tank of a flamethrower is dangerous when the flamethrower is in operation. It isn't dangerous (more accurately: not as dangerous) when it's not in operation. Without a substantial nearby ignition source, the fuels used in combat flamethrowers are very stable.
Note #2: commercial flamethrowers, like those used to burn weeds, use liquids like propane that become a gas when emitted. Faster heat, lower range. This might be the type of flamethrower you're thinking about where the damage is very local (less than one meter). You still can't do that with electricity. But at least it would be more believable from a suspension-of-disbelief perspective.
Brutal honesty: you're proposing a large spark plug as a replacement for a flame thrower. An electric discharge requires a termination point that's lower potential than everything else around it and there's no practical (or meaningful) way to create that lower electrical potential remotely. This is why electric discharge weapons don't work today as a means of offense.
Caveats: You could use an electron emitter as a directed energy weapon, but that means you're delivering charge, not necessarily heat. A strong enough electron beam could start a fire. It could cut through the concrete... however the battery required to do that is much more dangerous than the tank of combustible material. For one thing, it's a lot heavier and on the other, disrupting an energy storage device of that size has dramatic consequences.
Note #3: I can't underscore the problem of the battery enough. You could hand wave it, but the truth is that the rules of physics are brutal. Casting energy for the purpose of bulk damage requires a lot of energy and batteries simply stink at that. And when they're pierced by gun fire, they have a much higher chance of catastrophic discharge, which doesn't require a nearby ignition source.
Electricity is great for point solutions such as tasers or rail guns where the electricity is used entirely locally. But given today's technology, it's useless for direct remote attack of any form.