Can I transfer my Injustice game data from my iPhone to my new Android phone?
Man, you're out of luck. Versions of Injustice for Android and iOS differ greatly. the iOS version generally gets updated months before Android. This affects what characters you can buy, what challenges you can complete etc. 

I thinks it's safe to say they're incompatible. And from my experience the Android version performs rather poorly compared to iOS. 

Considering all of the above I would recommend sticking to your iPhone for playing Injustice.