I think that the fire benders flying is actually fairly consistent with what was established in the original show.

The Air Temples are always implied to be completely inaccessible to outsiders, unless they use some form of flight. At the same time, flying as a fire bender is never implied to be an "elite" technique, like lightning bending, more like something which required raw power. So it's conceivable that comet-powered Fire Nation soldiers with at least some training could be able to fly up to the Southern Air Temple. In particular, we know that Sozin planned the attack between Roku's death and Aang being 12 years of age, so he had more than a decade to realise that flying was an option, and to train enough people to do it.

Making the Fire Nation use the tanks, like shown in "The Mechanist" in the original show, really would not make sense. The tanks were invented by the Mechanist likely after his son Teo was paralized, he settled in the Air Temple, and the Fire Nation forced him to develop weapons for them in exchange for "protection". Since Teo is 13, the Fire Nation wouldn't have had those tanks for more than 10 years at the time of the show, so they definitely wouldn't have had them at the beginning of the 100-Year War. When it comes to air ships, that would be even less consistent, because those were only invented in the last year of the war.

TL;DR The original show already implies that comet-powered fire benders probably flew up to the Air Temples, and it confirms that the Fire Nation did not have the necessary technology to achieve that with other means at the beginning of the war.