This isn't possible in TweetCaster currently.
Twitter used to treat direct message compose much like regular compose, which allowed adding images to a third party provider. The issue was that the image wasn't private (so anyone who went to that user's page on the third party's site would see it). Twitter didn't allow images either and we changed it to match that functionality.
Recently, Twitter added direct message images to compete with the likes of Snapchat and Instagram direct, but did not open the API to do that to third parties. So we can't use that functionality right now.
In a recent update, we added the ability to view and preview twitter images in direct message threads, but we can't add images. If Twitter ever opens it to third parties though, we would add it.