How do I clear cookies from the Twitter app internal browser on iPhone? Just to clarify, I've tried cleaning the Safari cookies with no success.
I don't believe there is anything you can do sans uninstalling and reinstalling the Twitter app.   Each application that uses the WebView has its own cookie store.

A developer can programmatically remove cookies.  So the Twitter app would need to give you a way to clear cookies which I don't think it does.