For the Pom-Poms, a mixture of both armor piercing and high explosive shell would seem to be wisest. Tesla weaponry along with plasma and laser weaponry would work well against them, too. But Winchesters, revolvers, Mauser automatics, shotguns, and Lee-Enfields? Not effective is my guess. Even a belt-fed machinegun might not work, too. Plasma, Tesla, and laser small arms should work, too.
Probably biplane fighters would be useless. Perhaps a Victorian version of a Nebelwerfer or Stalin Organ multiple rocket launcher might work. Dragons aside, does the aerial kraken have any natural enemies? Or is is an APEX predator.
Tanks like the FT-17 should work and of course, the Mechs of Iron Harvest would be the aerial kraken's worst nightmare.