Kinsta does offer free migrations, but this doesn’t include migrations from other platforms such as WordPress.com to WordPress.org. These are two very different solutions. Read more about the differences in our article on WordPress.com vs WordPress.org.
You’ll need to utilize the WordPress.org self-hosted solution to use Kinsta’s hosting. Check out this tutorial on how to move your WordPress.com site to WordPress.org. Or you could also hire a WordPress developer if you need additional assistance.