Can Find My iPhone app track other devices with different Apple ID?

They would be under the iCloud account that goes with the Apple/iCloud ID signed onto the device. You would sign onto iCloud.com with that Apple ID and password to see the device under Find My iPhone.

Cheers,

GB

Yes the Find My iPhone app can track different ids. To logout of one apple I'd in Find My iphone , GOTO the app > (track the devices) then when you want to track another I'd, press Sign Out in the app and then login with your other I'd.