Q: Is it possible to transfer videos from someone else's iPod to my iPhone?  How do I accomplish this?

Depends on the model of iPod exactly.

If the iPod supports it you could try using AirDrop: How to use AirDrop with your iPhone, iPad, or iPod touch - Apple Support

If not there are Apps in the App Store that will allow you to send files including videos taken with the iPod and that reside in Camera Roll to other devices.

https://itunes.apple.com/us/app/photo-transfer-app-easily/id365152940?mt=8

Photo Transfer App allows you to quickly copy photos and videos between your iPhone, iPad, Mac or PC using your local wifi network.

You cannot send videos that are stored in the default Apple Video App.