There is no 'log out' method within AvPlan EFB.
If you are moving to a new login, simply log in using the new credentials.
If you are changing devices, set up your new device first (i.e. download AvPlan EFB, sign in, sync your aircraft across, etc). When you're happy with the new device operating correctly, uninstall AvPlan EFB from your old one if it's not going to be used as an EFB any longer. To do this, from your Home screen tap and hold on the AvPlan EFB icon and release when you see the icons begin to shake. There will be a small x in the upper left corner of the icon. Tap it to begin the uninstall process.