Looking at the specs for the rBlink, its outputting 2.15Vrms presumably this is for both channels combined. I can't find anything concrete on the iPhone 5 output, I'm found a couple of sources which quote 1.01Vrms but it's not clear if this is for one channel or 2. Either way the output on the iPhone is less than what the rBlink puts out.
Another think to consider, when you have your phone connected to the amp via cable do you have the volume on the phone turned up?