I would argue that chickens are less prone to motion sickness, not immune. Found a relevant response from an alleged animal behavourist on JustAnswer, which, considering this diagram I found, seems logical enough since it's not too different from the inner ear system we're well-familiar with.

Based on anecdotes and what people have discussed on here so far, I'm inclined to believe that for the most part, birds are not as affected by motion sickness as us humans (not necessarily because their heads can stabilise like chickens) because obviously they gotta manage some pro gamer moves midair when they're flying without getting vertigo (for flying birds at least), but it doesn't mean that they are free from it. Staying stationary in a moving vehicle isn't a phenomenon that occurs regularly in nature nor has it been until a few decades ago.