How do you logout on the gmail mobile app for iPhone
Access the menu screen displayed on your Gmail account and scroll down to the bottom of this page. From the list of commands provided, you will get the sign out option, which you are required to click on. Press "home" to get back to the main menu.
Go to the menu, scroll down and press "All Mail", close the menu and scroll down to the bottom of your messages and press "Log out" PRESTO!
Search sign-out button on bottom of the page