I'm guessing there would probably be some way to do this with IFTTT/Zapier or a similar service, but I haven't managed to do it, so it may need advanced configuration.
The problem is that IFTTT/Zapier requires the image URL to tweet. So maybe if you first create an action that takes a picture, find out a way to upload it to a server, get the URL, and add it as a variable to tweet... It could be possible, just sounds very complex.
If you can't find a way to do it out of the Flic app, we'll add the feature to the list of suggestions and contemplate it for future updates! Feel free to add it to ideas.flic.io so others can suggest/support your idea too.