How you insulate the knee wall cavity is determined by if you want the space to be a "conditioned" or "non-conditioned" space. A conditioned space is basically part of the building envelope and is heated and treated as the rest of the interior rooms. A non-conditioned space is considered outside of the building envelop and treated like an attic. One item that is consistent with both designes is that continuous soffit to ridge ventillation must be installed and available in each rafter bay.
If you still want the space for storage yet don't want to heat (non-conditioned) it then you definatly need to insulate and airseal the floor to keep the warm moist air from the bedrooms below from escaping up into the space. To do this I suggest removing the floor boards, insulate and airseal the cavities and then reinstall the boards. Of course the backside of the bedroom wall also requires insulating and airsealing then as well. Here's an example
of this type of non-conditioned space.
will show you how to handle the space depending on how you want to treat it.