A kitchen-sink overflow sounds like a mess! Hopefully you are able to get that cleaned up soon. Water damage that is caused by an overflowing sink is normally covered under home insurance, so the damage to your hardwood floor would be covered.
Many people hear the term “water” and automatically think flood, which is not covered under a standard home policy. The difference is that a flood starts outside of your home — for example, from a heavy rainstorm or a rising river. A kitchen-sink overflow is considered a “sudden and accidental” event, so typically it would be covered under your policy.