I have downloaded some images of an adult nature onto my phone. My problem is, they show up as preview images whenever I try to compose a new tweet in the official Twitter app. I can't find any setting to turn this behaviour off.
Your best bet is probably to use an app like Keep Safe to hide "adult" photos/files. This keeps other apps from being able to see/interact with them, so they won't show up in the preview section of any apps.
Create an empty file with the name "".nomedia" in that folder and new previews will be generated.