It really never was a important weapon in the german arsenal, there was better ones.
but it was produced in numbers on special factory-lines. regarding fire-weapons in an anti-tank role: as the offensive opportunities vanished during the war for the germans, flamethrowers were occasonally used to fight against tanks. the flammenwerfer 41 was produced in numbers of nearly 80000 and despite some counter-offensive activities (adrennen-offensive f. e.), the close combat anti-tank role was one of the more useful tasks for these weapons in the latter phase of the war for the german side. but I guess also a lot got lost in combat.
this technique came up in WWI and was sometimes effective, but with the mentiones disadvantage of the relatively short range.
the modern german army uses a discardable single shot device that is filled with phosphorous (Handflammpatrone DM34) and can hit tanks up to 80 meters. under very ideal conditions, afv can be knocked out. so the idea of fighting a tank with fire is not too odd.
jens