Yes the N1K2-J and all other variants of N1K Shinden Series had the automatic butterfly flaps.
source: Japanese Aircraft of the Pacific War, by Rene Francillon, ISBN #: 0-87021-313-X
Best Japanese Aircraft Book I have seen yet, pick it up, well worth it.
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Vermillion
WB's: (verm--), *MOL*, Men of Leisure, Goldlandia
AW's: (verm) ACCS, Aerial Crowd Control Services, Cland