So I know that the OFM(And thusly Bug!Kai) is an Omukade/Centipede monster, but considering that:
A) The Omukade/Centipede Monsters from Ninjago (the Series, not the place) are part human/transformed humans, which are omnivorous
B) They probably need to eat more than just people, considering OFM would of probably starved otherwise
C) They are both miriapoda
I think we can give Kai some millipede traits too.
Namely, I think Kai should be obsessed with eating cucumber (Millipedes love cucumber, to the point of getting addicted to it, even if itisn't healthy for them) as well as liking fermented foods in general (a lot of millipedes are primarily detritivores, which eat rotting plants and/or animals + poop. Millipedes specifically mainly eat rotting plants)
He has eaten all of the cucumbers Zane was going to put in a salad at least twice now.
He's also willing to try the occasional Frogfolk and/or Mucoid recipe- not Mr Frohicky's Fetid Swamp Tea, but there is a Mucoid recipe for fermented carrots that he likes snacking on, and there's a Swampwater Dumpling stand that he swears by (Roast Cricket and Swamp Greens, with just a touch of fermented Algae).