It would seem to me that if one knows something, besides the knowing itself, there should also be the knowing of the knowing.
You are approaching infinite regress. ^^
Without the knowing of the knowing, there can be no registration of anything by the knowing. If there is no registration by the knowing, there can be no retrospection.
What I was saying was that the reflexivity should be part and parcel of knowing itself because without the reflexivity, knowing cannot be knowing.
Actually perception / recognition / sanna is one of the seven universal mental factors and so is part of the typical cognitive moment in Theravada Abhidharma. But its not "part of the knowing" since knowing doesnt have any parts, its just an accompanying factor. The citta in TA is seen as paramattha dhamma / as absolute reality [constituent], which means that it has only one self-characteristic which in this case is illumining an object / cognizing. To follow the argument in Kathavatthu the citta would - to cognize its cognitive aspect - need to have two cognizings or there would need to be two cittas at the same time. which are both not accepted in TA.