depending on your requirements you could look at something like this for Unity Engine https://www.assetstore.unity3d.com/en/#!/content/10693
There is also a Plugin for the Unreal 4 Engine called KINECT 4 UNREAL FROM OPAQUE MULTIMEDIA
But if you have to write it all by hand for yourself, i have done something similar using OpenGL.
I used Assimp http://assimp.sourceforge.net/ to be able to load animated Collada models and OpenNi with NiTE for skeletal tracking. I then used the rotation data from the Nite skeleton and applied it to the corresponding Bones of my rigged mesh, overwriting the rotation values of the animation. Don't use positional Data. It will strech your bones and distort the mesh.
There are many sources for free 3D Models, like TF3DM.com . I for myself used a custom Rig for my models to be suitable for my code. So you might look into using Blender and how to Rig a Model.
Also remember that the Nite Skeleton has no joint for the Pelvis, and that Nite joints don't inherit their parents rotation, contrary to the bones in a rigged model.
I hope this helps to have something to go on.