Go to the App Center in your Settings area.
Scroll down below existing connections and select Install More Apps.
Select the Tumblr icon.
Tumblr will ask for your authentication details. Once you have successfully logged into Tumblr, the connection to Tumblr should show up in your Destinations with a status of "connected."
Once you are integrated with Tumblr, Kapost allows users to publish HTML (normal blog), videos, photos, and photo galleries. Again, click on the corresponding link to learn how to publish to each content type.
To learn how to create a Tumblr Content type, read this article.