I am looking for an iOS application that can show the battery charging rate in mA. Free if possible, and supporting iOS 7.1
The Tesla Model S app does exactly this. It shows battery charging rate for your car rather than your phone, though, which might not be exactly what you wanted.
Edit: the app is free, but the car is not...
The app ChargerTesting does this now. https://apps.apple.com/gb/app/ampere-charger-testing/id1438386754
It’s clever, has a few usability glitches, and Takes a while to produce a result, which should be taken as a ballpark figure rather than anything precise. But it does give you an idea what’s going on.