Its is a regrettable fact that there is no way to get Backup Asst. on these phones. Another unfortunate choice by Verizon.
You can try taking the old phone, and new Kin into a Verizon store, and they can attempt to transfer contacts there.
I had heard that some stores have the hardware/software means to do transfers to the KIN's, and some don't. Also worth pointing out some staff know how to do it and others are clueless.
Judging by potins in these forums, some people have had success this way, others have not.