Why won't zones flood into vias or other plated through holes that are part of a footprint in Ki-CAD
The zone settings for your connection have a 10 mil clearance and 10 mil spoke width.  This prevents the fill from being able to form a thermal spoke to the via.  One way to adjust this is to change the settings of the thermal via pads to be solid connection like this:



You will need to do this for all thermal vias in the footprint.

Alternatively, you can reduce the clearance size to smaller than the thermal via spacing in your zone settings.

-- Edit --
As Rene notes in the comments, you could also set this to (or leave it at) "From Parent" and ensure that the footprint Local Clearance and Settings is taking the connection type from the zone rather than forcing thermal vias.