To delete your post, the button is actually up closer to the top. The area you're looking at along the bottom just tells you what things you have permission to do (anything with a checkmark is something you're allowed to do).
Go to your post, and look in the orange section where the title of your post is. On the right side, there are several buttons to choose from, including edit, reply, and delete. Click on the delete button to delete your post.