Not a full answer, exactly, but enough additional comments to the answer by @Ack that I thought I could get away with it.
Just to reiterate, you don't need fire rating, unless the kitchen ceiling happened to abut a different unit within the house. Then I'm not sure.
1/8" - 1/4" out of level is pretty subtle. It would be noticeable if there was crown against the ceiling, or if your upper cabs were close. It would also be noticeable if it was 1/4" inside a couple of joist bays. If you didn't strap the ceiling, you could fix the cabinet/crown problem with mud.
Here's an answer I wrote a while ago about strapping ceilings. (Paradoxically, it wasn't the right answer to the question, but it fits your application.) SE answer on strapping ceilings. Strongly suggest you lay hands on a laser... I'm not going to go back and edit my old answer, but at this juncture, I'm not sure how I'd do this efficiently with a level. And definitely use 1x4s. They won't cost much more and give a lot more wiggle room for seams.
Edit, to your additional question, "how out of level is acceptable to not be visible?"... If you have crown up against the ceiling, or upper cabinets within 1", I'd say you want to be within 1/8" for the whole ceiling. If you don't have that situation, I'd shoot for 1/8" within any given 3' span. (It really isn't hard or time consuming to get a ceiling dead flat...)