Nuke, please, dont listen to Krusty now. Even though i havent spent much time in either of them... still, my observations:
-both planes without flaps, the spit (any) easily turns inside the niki. An other thing is, while the spit gains a lot of turn radius by using the flaps, its turn rate decreases drastically, from ~15.5 seconds per circle to ~17.5-18 second. The niki does a circle in 16.8-17 seconds without flaps and in ~ 17.5 second by using them. Their turn radius is roughly the same in both cases. So in a flat turn, the spit should keep his energy, without flaps it easily beats the niki.
-in a scissoring dogfight, the japaneese plane has a very minor turn radius and turn rate advantage, but also some disadvantage in the roll rate - might be more difficult to reverse at the top. And it doesnt matter which plane you fly, always use full flaps in a low speed (vertical-style) rolling scissors situation, as the turn radius and stall speed counts a lot more here than the raw turn rate.
After all, yes, the niki should definiately use its flaps.