How do you position your middle finger when closing the 2nd hole down from the top of the flute? L2 for us right handers. I find the bent position more comfortable but have been advised that flattening the finger out to close the hole more with the pad of my finger than the tip would help me seal the hole better for a stronger, more robust sound. Flattening the finger feels awkward and I’m wondering if I should push to adopt or if I should stick with what’s comfortable. I am curious about how others approach this finger position.
Do what is most comfortable for you! Everyone’s hands are different. But it has to be effective, of course.
I personally use a position about half way between the two you outlined, because that is how my fingers line up best with the holes.
I have noticed that Harry Bradley uses a position like yours, and it certainly doesn’t seem to hurt his playing! He makes all kinds of “mistakes” in his posture, but sounds brilliant! 
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And just for balance, here is Conal O’Grada doing it all wrong the other way!
My own finger position is more like this:
Unfortunately, it doesn’t make me play anywhere near that well though!
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I think my L2 & L3 finger positions are sort of in-between your two pictures. Initially I played more on the tips, but I’ve moved flatter with time. I’ve observed a number of better players using the hold even flatter than the one shown in your second picture. My last finger knuckles barely reach flat, unlike some guitar players I know when playing bar chords.
My right-hand fingers are closer to a piper’s hold, but not the left
I might imagine that flatter fingers could flap down with more force, but I’m not sure that matters.