You're not seeing things, that flap is really there.
I have not made an Inuyasha costume myself, but I'd probably sew it in at the left hand side seam and wrap it across after tying the kimono shut somehow (maybe little ties like a karate top or something would work). I'd probably use red Chinese frogs to close it (search google for frogs), or perhaps velcro or snaps, or even make a small red tie to tie it shut at the right side.
Or, you could just go without it. A lot of people do that (for example, I can't tell if that link has made their costume with it or without; the red all blends together).
~Anime North 2013 Masquerade Director [Masquerade AT animenorth.com]
~ Anime North 2013 Fashion Show Assistant Director [fashionshow AT Animenorth.com]
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