Okay, the only reason I would logically suspect that Shinn beat Kira would be that it was a 2 vs 1 fight with Rey involved. I mean, Rey isn't that bad of a pilot being clone of Rau. I'm sure Shinn and Rey will cover each other since they're good buddies and know each other well. When you think about it, Shinn charges in and does what he can, gets new parts when damaged while Rey covers him throughout the fight. Shinn will prevent Freedom from getting close to Rey.
This is my prediction of the battle and the reason why Kira EVENTUALLY is defeated. I believe Kira will make them go through hell for this one.

In the small pictures to the left, you see Shinn and Rey in their MS.

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