One time I tried using the Yahoo! Mail app I recently downloaded on my android phone to see its functions and possible new features. But as I went through the app, I noticed that there was a missing feature: the sign out link. I tried clicking various links to see if the sign out link is imbedded in them to no avail. In the end, I did what I do most of the time when things go out of hand – reset things.
For the Yahoo! Mail app, what you can do is to go to the Accounts and Sync under the Settings menu and delete your Yahoo! Mail account there. This will effectively sign you out of the app. But I observed some lagging so better wait until the sign in page appears again, as shown above.