how can I install find my phone on iPhone 3GS running iOS 6.1.3

Go to Settings > iCloud and turn on Find My iPhone.

iCloud: Troubleshooting the Find My iPhone app

http://support.apple.com/kb/TS3376

The current version of the Find My iPhone App requires iOS 7.

See this: http://support.apple.com/kb/HT5919?viewlocale=en_US&locale=en_US for possible older versions.

Note that you do not need this App installed for "Find My iPhone" to work. This App is only used to find an iPhone on an iPhone or iPad. You can find an iPhone on any computer by going to http://icloud.com in a web browser.

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What does having a front facing camera have to do with installing the Find My iPhone App?

You will notie I erased my post. I was responding to a different thread, and realized my mistake almost immediately. Thanks for pointing out my stupidity.

That's OK. Feel free to report my stupidity whenever required. 😉