Passing node id as contextual filter to field collection view
Please try the following. 


Add a relationship "Field collection item: Entity with the {Field Collection name (field_collection_machine_name)}" You should change the one in {} with your filed. 
Now you should get the content nid in the contextual filter which could be used to filter using the node id.
To limit it to show only the flagged fields you should select the "Flags: Field collection item flag" from the relationships and select the flag you want to filter it by and select if it should be for the current user or all users