Tumblr messages are essentially private correspondence between one user and another. Referred to as Fan Mail, these private messages encourage one-on-one text communication. Direct image insertion is unsupported in private messages through Tumblr.
Fan Mail Messages
When sending or replying to a Fan Mail message, you're limited to changing the paper background image and font. Although you can't add images directly, you can include an image link by uploading your photo to an online hosting site and copying the link into your message.
Another option like private messages is the Ask feature, which enables readers to send a question to you privately through your Tumblr. You can choose to respond in private, which appears in the asker's inbox, or publicly through your blog. Either way enables you to add an image in your response with the Upload Image option.