I'm from the UK and I would naturally pronounce it "KINGZ-b(uh)ree", where the "uh" sound is weak and tends to get swallowed up. I've noticed a difference in the way many Americans pronounce "-bury" in names, often pronouncing it as "berry", with a prominent "e" rather than the neutral "uh" sound that you find over here. Hopefully an AmE speaker will be along to give their opinion.
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