After migrating from heroku to dokku, we had to also chance codeship so we deploy to dokku. I followed the following steps to successfully deploy to dokku.

1. Save the public key of the codeship project. It is found in Project Settings > General Settings.
2. Copy the public key to a file /tmp/codeship_projectname.pub.
3. Make sure when pasting, all the contents are in a single line and not multiple lines.
4. Add the public key to dokku using the following command in console. Reference.

cat /tmp/codeship_projectname.pub | ssh root@yourdokkuinstance "sudo sshcommand acl-add dokku [description]"