I know this is old, but your Flywing is actually only a 98cc. Owned one, look at the casting number & you'll see what I mean. With this being said, W&G's carb suggestion may be a hair too big. Might try a PZ19-PZ22 carb IF you swap Here's what I would do though:
Ebay sells complete carb rebuild kits for $10. The Flywing is a little bit of a different animal when compared to other pit bikes. It's actually based on a Yamaha PW80 where most are based on the Honda CRF & XR lines. The carb hat that connects the throttle cable to the needle is unique too and it has a Walbro carburetor instead of the typical Keihin so be aware.
Biggest downfall of that bike is probably the 2 stroke exhaust on a 4 stroke bike. Made no sense to me.