The best (and easiest) way to set up an email signature in your Gmail App on iPhone or iPad is to do it by using the web-based version of Gmail on your computer. When you do that, your email signature will automatically be appended to all your emails sent out from your Gmail App on your iPhone. This is done by the server-side processing of your emails on the Gmail servers. Simply log in to your Gmail account, and install the email signature through there.
When you do this, make sure that your mobile signature is turned off in your Gmail App on your phone. Otherwise, it may conflict with the one you set up in webmail, and may not work correctly. To turn mobile signature off in the Gmail app, go to Settings, Select your email account, Signature settings, Set Mobile signature to “Off”.