The Middle Flathead is a nice couple of day run. For the flight in try Eagle Aviation in Kalispell. The river is not too complex. At high flows the rapids are pushy with big holes, at low flows they are more technical. I think Western Whitewater has all the beta you need.
I've paddled from Moccassin Creek to Glacier NP border when flows were around 7,000 cfs (early July). It is a beautiful cold water paddle. I guess it gets a class III rating at 3500 cfs, and at 7,000 I'd say it is big water class III-III+ with maybe two rapids that are IVs. There are a few holes that can easily be avoided (although I failed to do it on one of them). As for the upper portion, we decided not to do it because the cost of the trip, etc.
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