What is the state of the art for k nearest neighbour search?
It seems hard to imagine that your claimed running time is correct, for a method that works in an arbitrary number of dimensions.  It sounds like you are claiming that your data structures works in an arbitrary number of dimensions ($n$), but the running time does not depend on the dimension ($n$). That seems unlikely; nearest neighbor search is known to be hard to solve in high dimensions (the so-called curse of dimensionality).

Alternatively, if you meant that your scheme works only in 3 dimensions, then that is an important caveat that needs to be mentioned.  Being able to find the nearest neighbor in 3D in $O(1)$ time would be an impressive result; I'm not aware of any data structure that is known to have this worst-case running time.

Yes, a k-d tree is a standard data structure for this task, when you are working in 3 dimensions.  There are also generalizations and related data structures; see metric trees, binary space partitioning trees and octrees.  R-trees and R*-trees can be used if the set of points are changing.

Without knowing how your algorithms works, it's hard to give a definitive answer whether it is worth publishing.  To figure out, a good starting point would be to familiarize yourself with the published and known algorithms and see if your idea still seems to be better than all known schemes.  If you're still not sure, make ask a new question here with the specifics of your algorithm and what your specific uncertainty is.