How to get a flat band frequency response with an inductive input
Here's a few things I've tried:
  
  
  Place a reasonably large resistor R3 in the non inverting input to decrease the quality factor of the LC tank which should smooth out the
  frequency response
  


I tried the same idea, but with resistance in parallel with the pickup coil instead of in series.

I used an LT6202 for low noise and a suitable bandwidth. The 2 pF capacitor represents estimated stray capacitance in the pickup coil and wiring. 



Frequency response is flat within 1dB from 100 kHz to 15 MHz. Note how the op amp's high frequency rolloff flattens out the peaking coil response. 



With an input level of 1 V rms the signal to noise ratio is ~40 dB. That's only about 6.5 bits of ADC resolution, but could be greatly improved by oversampling and/or better coil coupling.   



Of course this is only a simulation. Real-world performance will be critically dependent on coil characteristics.