Yes, rat fuzzies are about the equivalent of a weanling or small adult mouse. It would be better to stick with mice if you can get them (the specialty store is your better bet; big chain stores only seem to carry the most basic sizes i.e. pinky/hopper/adult), since rats are fattier and a rat fuzzy is going to have underdeveloped bones/less calcium.
As far as him getting picky, it's not all that likely. King snakes, especially, are opportunistic and tend to not be picky at all. If he does get stuck on rats for whatever reason, it should be simple enough to switch him over by scenting the mouse in rat bedding or rubbing it on a rat.
I'm not sure that chicken would be an acceptable diet. Being just muscle meat, it doesn't have the nutrition from bones or organs. You can add a calcium supplement to make up for the lack of bones, but the organ meat... I imagine that would be much more difficult to compensate for.
If he goes off feed for whatever reason, anyway, you're going to have better luck figuring out why he stopped eating in the first place and correcting that than you would getting him to eat a slab of chicken.
If he ever does decide to go off feed and it's just a winter or breeding season thing (not a problem you can fix), you can either wait it out or tempt him with scenting. Chicken broth is, actually, one thing used to scent mice, and successfully at that. I wouldn't go so far as to offer him a slab of chicken, but you can probably use some of the juices from your chicken to scent a mouse if he ever decides to be a snot. (Other scenting methods include scenting with strong-smelling mouse bedding, rat bedding, tuna juice, lizard, other snakes, washing with a mild soap so it doesn't smell like people...)
Okay, seriously. I'm getting VERY curious why "j e r k" is considered such an awful curse word on this forum that they actually censor it. Considering that word is a standard part of my vocabulary, it's getting a little obnoxious... Lol!