See the documentation for the AirflowNetwork:Distribution:Linkage object. The following output variables will give you mass/volume flow rates between nodes in an airflow network:

HVAC,Average,AFN Linkage Node 1 to Node 2 Mass Flow Rate [kg/s]
HVAC,Average,AFN Linkage Node 2 to Node 1 Mass Flow Rate [kg/s]
HVAC,Average,AFN Linkage Node 1 to Node 2 Volume Flow Rate [m3/s]
HVAC,Average,AFN Linkage Node 2 to Node 1 Volume Flow Rate [m3/s]

I haven't tried this myself, so it may be possible to do this with AirflowNetwork. However, it may be difficult to get the network to behave as desired without basically overspecifying the problem (i.e. setting the flow rates), in which case the pressure network is overkill. I doubt that the solution will involve AirflowNetwork:Distribution:Linkage since that is used for distribution systems. How complicated is the building, and have you experimented with the example files that implement Trombe walls? Depending on what you're trying to do, this might work out just as well.

The minimal AirflowNetwork that might be able to get you something like you want is to use two surfaces, one high and one low, to represent the partition between the Trombe zone and the interior zone. Simplest thing to do would be to divide the partition in two, which won't quite have the heights right (the airflow calculation uses the elevation of the center of the surface), but it's a place to start. Create a AirflowNetwork:Multizone:Zone for both of your zones, attach a AirflowNetwork:Multizone:Surface to both the high and the low surface, and then attach a leakage component. You probably need to connect to the ambient to get a good solution, you can do that with a high resistance component connecting the interior zone to the outside.