Add a config variable (called $wgFlowReadOnly or something) that, when enabled, will cause all attempts to edit/create Flow boards/topics/posts to be rejected, regardless of user rights or global user membership.
This is not easily achievable through the normal permissions system, because different wikis assign flow-create-board rights to different groups, and several global groups have this right, but we can use the getUserPermissionsErrors hook in MediaWiki to achieve this.